I'm not aware of any specified camping areas actually around Lake Dobson - I think the lake and direct ski-fields area are "day-use" only (but you might want to check the Parks website to make sure).
If you don't mind a little walk, you could get up to the ski-fields and try and find a tenting place over near Mt Mawson (between 30 - 60 min walk, mostly on 4wd track).
In the "downhill" direction, you might find some camping spots on the edge of Platypus Tarn or the river exiting Lk Webster.
There's always the "official" campsite back down at the park entrance - but that will cost $$$.
Some cheap-and-cheerful huts exist at Lk Dobson too which Parks manage ($40 for up to 6 adults)
http://parks.tas.gov.au/index.aspx?base=412#mt