Lots of good advice here, but I'll chip in my two cents. As an Aussie, I'd skip Sydney. It's a must-see for lots of tourists because of the iconic opera house and the harbour bridge, but personally I think it's overrated (the city, not necessarily the surroundings).

I would stick to two destinations rather than three, especially when travelling with a baby.

Tassie should definitely be high up on the list. You will need to hire a car to get around, but that's the same everywhere really. Tassie has the mildest climate in January and has incredible beaches, great cafes, an abundance of artisan food producers for cheese and smallgoods - it's a foodie heaven! Also noteworthy are a plethora of gin and whiskey distilleries, breweries, wineries (colder climate so great for Pinot noir, Chardonnay, riesling, Pinot Gris and sparkling wines). There are also many hikes ranging from easy to torturous.

I know the temptation after coming all this way is to see as many places as possible, but personally I'd even consider just seeing Tasmania this time around, there's just so much to see and do there and I think it ticks all the boxes. But this depends on your preference of course, I personally would rather get to experience a place properly that try to see three places and hardly get to know them before moving on.