There are quite a few academic competitions (national or state) available each year. Some of the ones DS1 and DS2 have entered (and I can recommend) are:
DS2 has now finished the round of ICAS tests for this year, an annual routine we commenced many years ago when DS1 was in Year 3. The ICAS (International Competitions and Assessments for Schools) tests are run by Educational Assessment Australia (EAA), an educational non-profit group of the University of New South Wales (UNSW) that specialises in large-scale assessment programs in Australia and more than twenty countries internationally. ICAS tests cost a small fee and are available for Digital Technologies, Science, Writing, Spelling, English, and Mathematics.
Most schools (I think) offer some ICAS tests - in our local Primary school they used to offer the whole suite of ICAS tests to interested pupils, but recently have reduced it to only English and Mathematics. I suspect this is due to low participation rates (only around 8/40 pupils in DS1s class did the ICAS tests this year) due to lack of interest (especially amongst those that don't expect to do well in such tests), having to attend the test before school, and the cost.
Fortunately the coaching school DS1 attends on Saturday morning is also able to offer ICAS tests in those subjects where it is not available at the pupil's normal school - so DS1 was able to do the remaining ICAS tests not available from his local public school.
Not really a competition, and not available to a student each year, the National Assessment Progam - Literacy and Numeracy, aka 'Naplan', is a compulsory test administered by the Department of Education every year, but only sat by pupils every second year (when they are in years 3,5,7,9). It is designed to allow the government to see how effective public education is in teaching 'the basics' of literacy and numeracy (English and mathematics) to the 'minimum standard' expected per the curriculum. The results are reported in 'bands' (1-6) for each year, in a similar way that 'bands' are used for assessing student performance in the HSC. Detailed results (showing student responses to individual questions, the correct response, and what % of the student cohort got the correct answer) are also provided, which can be a helpful guide if your child is having greater difficulty with one particular subject or one area within a subject. However, it is a fairly blunt tool at the top end, with DS1 and DS2 getting mostly band 6+ (the little triangular pointer which says 'somewhere above band 6...').
Young Scientist Competition:
This is an annual competition run by the Science Teacher's Association of NSW (STANSW) for students from years K-12 (there are separate categories for K-2, 3-6, 7-9. and 10-12). Entries can be in the category of 'Scientific Investigations', 'Models and Inventions', or in both categories. There is plenty of online help for parents and teachers at http://www.youngscientist.com.au/ and as entry is free it is nice way to introduce kids to the 'scientific method' and writing a 'lab report' without having to worry if the entry is 'competitive'. Every entry gets a certificate ('participation', 'commendation',' high achievement' or 'excellence' depending on the score) so all student efforts get rewarded. There are small cash prizes for the top entries in primary school categories, and some more substantial cash prizes (and trophy for the winner) in the senior school entries. Some winning entries also go on to the National Science and Engineering Awards and might be selected to proceed on to the International Science and Engineering Fair...
Logical Thinking Challenge (LTC):
This is a free online adaptive multiple choice test (24 questions in 30 minutes) run during one 24-hour period each year (12/13 September this year) for students in Years 3-8. It is developed by the University of Melbourne and achieving an excellent result 'wins' free entry into the Creative Problem Solving (CPS) written competition run by North Shore Coaching the following month. North Shore Coaching also donates $100 to every school that has more than 30 students participate in the LTC. See http://184.108.40.206/web_student/LTC2015.aspx for details and online registration.
Creative Problem Solving (CPS) National Competition:
Run by North Shore Coaching College, this competition costs $20 (refunded/exempt for those that do well in the LTC), this written test is set and marked by the University of Melbourne. Entries close on 6 October and the test is on 17 October. Trophies, Certificates and Prizes are awarded in each Age Group (A-F).
The Australian Mathematics Trust (AMT - see http://www.amt.edu.au/) runs both 'open' and 'invitational' competitions in the areas of mathematics and informatics. These competitions have to be entered via school registration. The annual 'open' competitions are:
Computational and Algorithmic Thinking (CAT) - for students in years 5-12. Held in March.
Australian Mathematics Competition (AMC) - for students in years 3-12. Held in May.
Australian Informatics Olympiad (IAO) - for students in years 7-12 with programming ability. Held in September.
Australian Statistics Competition (ASC) - for students in years 7-12. Project based, due in September.
UNSW Computing Department runs an annual programming competition (ProgComp) for High School teams around Australia. The main round is held in schools (19 June this year), and the best dozen or so teams get invited to compete at the Grand Final held at UNSW on 5 Sep this year. Teams comprise of up to three students. The competition involves solving as many as possible of around five set problems in two hours, using any programming language that will take input from keyboard or text file and produce output as a text file. The program code and text file submissions are manually reviewed to check that output has not been 'typed' rather than generated by a running program. The manual marking allows some marks to be awarded for partial solutions. Textbooks and manuals can be consulted, but no outside help is allowed.
DS1 has entered this for the past couple of years (using Python) and enjoys getting a better score each year, but as a 'team' of only one student, his entries aren't competitive. He might have more luck organising a real 'team' next year when some of the other students are studying Software Design and Development in Year 11... unless you make it to the 'Grand Final' there are no prizes, but you do get a certificate, and your name on the past results page: https://cgi.cse.unsw.edu.au/~progcomp/2014/home/pastcomps.php
There are school-team based 'round robin' competitions run by the NSWJCL (NSW Junior Chess League) during terms 2 and 3. There is also a one-day interschool chess competition held at the end of term 3. Aside from that, the NSWJCL also runs one-day, and two-day chess competitions during each school holiday. The entry fees are modest ($15 for a one-day competition involving 7x30 min games), but you also have to pay the small annual fee to join the NSWJCL (for which you will get the magazine each term that includes some Chess puzzles, articles about winners of NSWJCL competitions, and the printed chess ratings listing). DS1 and DS2 play school chess, but don't take it very seriously, so they only attend one (or two) of the one-day chess competitions during school holidays if they have nothing else organised.
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