Highway 1 which goes right round Australia is 14,500km. If you drive 800km a day, you will be able to circumnavigate Australia in just over 18 days - but you won't see anything except roads. You will travel through all the capital cities (except Canberra and Hobart) and each is worth at least a week, so we are now up to 53 days. Add a side trip to Canberra for five days and we are up to 58. Hobart and Tasmania will add at least a week so 65 days. There are all sorts of things to do on the way, Alice Springs and Uluru are worth the visit but they are not on highway ! so you will need to divert. Three days of driving and five days in the red centre will see you right but we are now up to 73 days. That leaves you 17 days for all the stuff that is not in the capital cities like the Great Barrier Reef, Monkey Mia, Phillip Island, Byron Bay, southwest WA, the Kimberley, Kakadu National Park. the Daintree rainforest, Surfers Paradise, the Barossa valley, the Murray River and all the rest. You don't have enough time.
Work out ahead of time what you want to see and allow enough time to see it. You can see a lot in three months but you won't see everything or anywhere near everything.