Good choice for a holiday destination. Tassie is amazing, I love it here. I always get that "wow" sigh thing happening when I see the mountains, snow, beaches... there is so much to look at!
There are heaps to do ... some free and some cost a whole lot more. Give yourself at least a couple of weeks, personally I would say a month. It does look small but there is a few hours between places, like Hobart to Launceston is a 2.5 hour drive.
If you can, stop along the way, there are great small towns that have cool thing to look at. Ross is stunning. Cambell Town has a great park for the kids, we always stop there to eat

As for activities and things to do...
Tahune Air Walk
Zoo Doo
Tasmanian Zoo in Riverside, Launceston
Port Arthur
Richmond gaol (and scenery in general is gorgeous there)
Wineglass Bay and Coles Bay
Launceston City Park (they have monkeys and a great kids playground and it's free )
The Gorge and Trevallyn Dam in Launceston are just stunning, the gorge has the longest chair lift.
King Solomon Caves
Tasmanian Devil Sanctuary
Tasmazia
Cradle Mountain, snow in winter
Cascade Brewery in Hobart, very interesting
Mt Wellington, the views are stunning there, snow in winter

Gosh there is heaps more. I am pretty sure you can go into a tourist place and get a list of things to do. I've been here for 10 years and there is still so much I want to do!!