I can confirm (as an Aussie) that if travelling in Jan-March you should stick to the coast and avoid the centre and north. With the exception of a lot of desert and Uluru there isn't much to see inland. Most of the tourist sights are by the coast or within 100kms of the coast anyway and you cann't go swimming in the Ocean if you visit the centre.
Take lots of sunscreen and water.
What you should see:
Sydney Area - Bondi, Manly, Blue Mountains (Katomba, Three Sisters)
Melbourne Area - St Kilda, Philip Island, Mornington Peninsula, Great Ocean road, The 12 apostles (now only 8 left)
Tasmania - all of it. Only takes 1-2 weeks
SW WA, Albany and the Valley of the Giants to Pemberton, Margaret River, Perth.
SA, Nullabor plains, Barossa and Claire valley if you like wine. Skip Adelaide.
Don't bother about Canberra.
Snowy mountains in Summer is great.
Tip when leaving Sydney going North:
I would avoid the coast roads from Wollongong to Brisbane. There are too many radars and too much traffic. Instead from Sydney if you go north take the Putty road to Hunter Valley then join the Old England Highway. You'll see reall country towns and not just coast roads. But that's just me... There are also great campsites on the coast and swimming.
When Going South you can also take inland roads through Kangaroo Valley.
You can't do everything but 3months is not a bad start.
Enjoy!