Mike, if you can get discount boat fares bringing your own car would be a good option (
www.spiritoftasmania.com.au), at peak times the fares can be quite expensive. Don't forget there's also the cost of travelling from Newcastle to Melbourne and return.
The nice thing about having your own car and camper is that you can vary your plan as you travel, (we're just completing our 4th driving trip to Qld and return and we have had no set itinerary, just gone which ever way has taken our fancy.)
Probably the cheapest way to go would be to fly and hire, you may find a fly drive package at a good price, if not you can get discount air fares from Sydney via jetstar and Virgin (Be aware that excess baggage is obscenely expensive), Red spot rental has good prices on cars.
The best weather is generally from late January to April, from April to November is the forestry burn season, the Northern area of Tas is often smoked out during that time.
Temperatures vary but are usually in the mid 20's to low 30's in Feb/March with low humidity, by the end of April usually hovering around the 20's. Night time temps at are cool, less so than inland NSW.
The weather from November to February can be quite variable, ranging from warm to cold and windy, often nice but unrpedictable.
The old saying goes "if you don't like the weather come back in 30 minutes".
As for snow, it can snow at any time of the year, but usually snow only falls in the coldest months (July to October but I've seen snow on Christmas day).
There are countless walks you can do, in any surrounds that take your fancy, from Launceston it's only 30 minutes to the seaside, 30-45 minutes to the nearest mountain, 1.5 hours to Cradle mountain National park.
If you're a wine lover, Tasmania offers some of the best wines in the world, there are dozens of wineries within the Tamar valley alone.
Both the East and West coasts (Strahan and the Gordon River Cruise as Al mentioned) are worth a visit, the beaches are unspoiled and mostly deserted compared to the mainland. Hobart and surrounds are also quite spectacular.
When I get back to Tas I'll get together a bit of a list with some photos so you can get an idea of some of the areas that you may want to visit.