Welcome to the forum D and you and your Bf should get plenty of sunny hot weather as you are arriving close to hottest time of year for Oz and that's February/March, so first of all get yourself some good shade hats, loose light clothing and sun protection 30+cream for if you're coming from a northern hemisphere winter you'll probably need extra protection.

Fraser Island is a great place to visit and to me it is the kind of place you could spend weeks, especially for great camping but seeing as you're time limited and it'll be hot there too, you're probably more advised to do what a lot of people do, and that's take a tour, they ranging from one day upwards and you can check a few here - Fraser Island Accommodation and Tours - Queensland, Australia
There are self drive tours arranged by a number of backpacker hostels at mainly Hervey Bay and also Rainbow Beach where six or eight backpackers get grouped together in a 4wd vehicle with camping gear for usually three days, but that sort of trip there is potluck as to who is in the group and who does driving etc., and hot weather ain't the best for camping.
More info here - Fraser Island, Great Sandy National Park - EPA/QPWS

It's a bit sad that you'll miss the Great Barrier Reef in northern Queensland but January/February is not the best of times to be heading too far north because of wet season possible storms/flooding and even cyclones but if you decided on hiring a car to go to Hervey Bay for Fraser Island tour, about another three hours drive would get you to Agnes Water/1770 and you could experience the GBR at LMI - Lady Musgrave Island | Great Barrier Reef Cruises |Scuba Diving and Snorkeling | Town of 1770 | Southern Great Barrier Reef but if thinking of that, it would be wise to check on the weather beforehand and take extra care when snorkelling (wear a Tshirt) so you do not get a lobster back - the hot sun!

The other attractions north of Brisbane are The Australia Zoo (Steve Irwin) and Noosa/Sunshine Coast, so on time allocation a whole week would be good value in that region going as far as 1770.
Whilst Brisbane itself does not have a great deal going for it, especially when hot and humid (it being far enough from the sea not to get cooling breezes) but a great complex at Southbank with pools, there's Discover Moreton Island - Queensland, Australia as an alternate to try some snokelling/feed dolphins and Koalas at Lone Pine Sanctuary - Lone Pine Koala Sanctuary and the guide gives you more info.

100 km. south of Brisbane there's the Gold Coast which is Australias premier holiday location with beaches, theme and wildlife parks etc., another place that you may not tire of in a few weeks, but beware as the beaches can be dangerous.

One way of travelling that could suit you if there are relocations to match your dates, would be to do some campervan relocations Brisbane to Sydney and Sydney to Melbourne - Rental Car Australia New Zealand United States Canada - Hire Now at StandByCars and that would allow you to stop at Byron Bay and then say Port Stephens with not too long a drive from there to Sydney.
The Campervans allow you to pull up wherever you can find a quiet spot and so you can save on accomodation costs too.

Sydney and surrounds you ought to allow at least 4 days, Darling Harbour, The Rocks area - The Rocks Pub Tour , Harbour Cruise and/or trip out to Manly, South Head/Bondi , a trip to the Blue Mountains being highlights.

If you do not do a campervan relocation, an overnight bus to Melbourne is one way to go, though sleeping in a bus is not a delight but you will stagger through the next day in Melbourne (make good use of the Free City Circle Tram to see all the city highlights - commentary sometimes and guidebook on board).
Highlights of Melbourne onclude a great bar/cafe scene in many different ethnic locations and tours to Great Ocean Road, and Phillip Island for more Koalas and Fairy Penguins - www.bunyiptours.com will give you some idea, and again about 4 days would be good.

Cheap Flights, Qantas, Virgin Blue, Jetstar - Cheap Flights & Airfares - Compare Flights at Webjet - Webjet.com.au or Welcome To Tiger Airways will find you cheapest flight from Melbourne to Perth and also register with Australian Travel Agent : Best Flights - discount travel - Travel Agent Australia to find out about any sales on, usually December for flights early in NY, and book direct online with airlines.
Perth has the SW region, the Swan River and also check out Rottnest Island, there being hostels there, and again 4-5 days to a week would be ideal.

You'll probably have to be making some choices on what you leave out, time and budget wise and if you just google up each of the Cities/States you'll get a heap more info too.
BUG*- Backpackers Ultimate Guide to Australia is a good guide for hostels when in the cities and if you hunt out the smaller ones, there's usually a few dollars to be saved on rates - Alfred Park in Sydney being one example.
YHA Australia is also a good site re checking good value tours etc., but hostels all have plenty of info on good backpacker deals.

Get yourself from hostels free copies of The Word and also Safari Petes Ultimate Guide, and they often have some good vouchers as well as info.

Have a great trip.