Australia is not only a wonderful country to visit but it is a country that has something for everyone, at every age, to enjoy and remember. The possibilities are endless and NO ONE will be disappointed.
Almost anytime of year is good to travel in Australia, mainly because it is such a large country (the USA would fit inside Aussie) so that you can find good weather for whatever you may want to be doing practically anytime of year.
As far as where to go (and how long) well 4 weeks is a good start for discovering and exploring Australia. You can get to the faraway places, for example, assuming you arrive into Sydney or Melbourne, such as Cairns or Port Douglas to get you to the MUST SEE Great Barrier Reef up in the northeastern part of the country. Then, you may wish to fly to Alice Springs and check out Ayers Rock and the Outback for awhile, and I would also encourage you to try and visit Perth (Fremantle) for more gorgeous views, sailing, sport fishing and the Indian Ocean side of Australia. You'd need another flight (a lot of time there are "air passes" one can buy for travel withing Oz) to get back east but I imagine you could add on another for not much and I if I recall correctly, there is a trans-Aussie train that would go to Adelaide, which is also a very fine place to visit - lovely city, interesting allure.
Some folks also like to go to Tasmania - I think you can do that by boat or plane..........everyone I know that did it, enjoyed it. I didn't have time to go to Tasmania because instead of doing an ALL AUSTRALIA trip like you're doing, I did Sydney (LOTS to do there - truly a marvelous, lovely, amazing city) and New Zealand and Fiji. So, while I was down there awhile, I spilt up my time a bit.
One warning - DO NOT TRY TO PLAN A ROADTRIP ON YOUR OWN INTO THE OUTBACK. It is not advisable as the weather can be brutal and there are often long stretches of road with no gas available (they haven't quite made it a transcontinental highway) or water/sustenance and hence can be quite dangerous. Use flights, trains or tours for long stretches.
Get yourself a good Aussie travel guidebook and start reading up on all the wonderful places you && your family can visit (kids might just LOVE trying out some surfing or boogey boarding at FABULOUS Bondi Beach near Sydney!) and then come back and tell us which places interest you the most and then you will get more detailed feedback on planning your trip. I have attempted to give you a more general notion for the moment just to assure you that the amount of time you've set aside is good and where to think about going - and I only mentioned the BIG cities - there are literally so many wonderful places to see and things to do, for kids & grown ups alike, in Australia.
When I was planning my trip - and I have traveled extensively to Europe and visited Asia, Caribbean, Mexico etc - I spent the MOST amount of time planning my trip to Australia and New Zealand. It warrants the time it takes to research and get to know the country and seek out what interests you most. We can work on it more as time goes by.
I personally cannot wait until the time comes when I can go back - to visit my dear friends in NZ and make more new ones in Australia as you truly cannot find nicer people on this planet than those Down Under!!
Only hard part is that trans-pacific flight but Air New Zealand made it quite comfortable (even in coach!) and tolerable, all down to about the last 2-3 hours when you really just want to GET OFF THE PLANE! But the rewards are great when you arrive and the flight will be a faint memory once the fun begins. I was indeed tired when I arrived but my very caring and helpful innkeeper, Mara Dimond, who then owned the Hotel 59 (they've since sold it) in Kings Cross (Kings Cross is not seedy as they say) made me stay awake (I arrived on a Monday morning in Sydney) after having a "wake up shower" and she then mapped out a great walk for me with the reward being that I'd made my way down and around through, among many things, the Royal Botanical Gardens which then opened up onto the spectacular site that is that gorgeous Opera House, Harbour and Bridge - simply breathtaking and I made it through the day, coming back to the inn and getting into bed early and made a relatively good transition to local time, recovering from the flight probably from the kindness of the people, the excitement of being there and the eagerness to explore!!
So let us hear from you again as you get an idea of what you'd like to do whilst in Australia. Look forward to hearing from you again soon!
I can't think of a NICER country for a family to visit than Australia - it just has it all!!