Sydney can be cool to cold in July - they do get a winter, even if relative to northern hemisphere UK/European/US winters it is relatively mild and be absolutely lovely up Cairns way and with three months you may even want to consider doing Alice Springs/Uluru and up to Darwin etc. and then over to Cairns and head south.
If you have not booked flights yet, I'd check on flying direct into Darwin if wanting to see the top end or into Cairns, there being Qantas and Cathay Pacific with HK to Cairns flights and I'd expect there'll be a few airlines that fly into Darwin as well.
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do KL to Gold Coast flights pretty cheap as well but still even cooler there in July.
Have a look at www,greyhound.com.au and Premier Motor Service - Home
as both those have bus passes and most coastal customers are backpackers and a lot cheaper than Ozexperience.
You might even want to have a look at YHA Australia
as they have had Sydney to Cairns fly one way, bus the other packages in the past if you're stuck with flying into Sydney.
An open Jaw ticket would be the go for you though.
And you will not have a problem following the backpacking trail - just keep an eye out for all the exhausted bods along the way, a great halfway rest up being 1770 Southern Cross Backpackers
, a little out of the town but in a great setting there.
I've heard that there's also cheap surfing lessons to be had there as well and Lady Musgrave Island is one of the best GBR locations owing to very much fewer visitors.