February is peak summer and after schools/universities are back. Can be very hot (by our standards). Humid in some places.
There are a lot of what to do - Aussie itineraries in this forum. Just go down the screen/pages.

A lot depends on what you want to see & experience and how much your budget is:- cities, wildlife, barrier reef, Aussie outback or ??

Having said that, February is too hot and unpleasant for the outback-central Australia. And not the best time for far north Queensland (FNQ). A bit south like the Whitsundays / Hamilton Island would have more pleasant weather and reef access. And easier with a junior frequent flyer. A very good time for Tasmania.

And you need to appreciate the size of Australia. Is sort of similar in size to the US 48 states. Considering from hotel, to airport, flight and to the next hotel it can take the best part of a day to go a destination. The day of arrival and day of departure you will not do much.

Airlines that fly in Australia domestically. Excludes some small operators
- Airnorth TL Regional airline in northern central Australia
- Jetstar JQ (a low cost carrier with low-medium-high priced fares owned by QF)
- Regional Express Airways (REX) ZL Regional airline
- Tiger Airways TT (a low cost carrier with low fares part owned by Virgin Australia)
- Qantas QF [OneWorld Alliance]
- Virgin Australia VA (Delta & AC* partner) *= ~2017 some routes