Perth can be seriously hot in January, and over recent years really humid too. Down south is beautiful and if you stayed in the Margaret River area it would be a bit cooler but its not cheap unless you are looking at caravan/park cabin sort of accommodation. Further south to Albany or Denmark would be good and a bit cheaper, but you would have to hire a car and that is going to put a hole in your budget. Rottnest Island is beautiful but again, accommodation isn't cheap (and definitely isn't flash if you stay in a cabin) and its very popular over the summer school holidays. You can often get cancellations from the ballot though. It is a really relaxed place though - mainly because there is close to nothing to do but beach sort of stuff. No cars so the world slows down and it is great for kids.

Given you're over east I would vote for Fiji too. Easily do-able on your budget I would have thought, and flights are short for you.