The challenge is to make it so that Tasmania is both a lot more populous than OTL (its population must be approximately 7 million, or more if possible) and more influential than OTL. It's up to you whether Tasmania is an independent nation (i.e. it refuses to participate in Federation, like New Zealand and Fiji did) or whether it is still an Australian state (in which case it's be a super-special-important state like NSW and Victoria in OTL).
There is no limit to how far back the POD is (but try to aim for no earlier than the mid-18th century at most) - the only requirement is that it is indeed the UK who colonises Tasmania (so you can't make Super-Tasmania Dutch or whatever, and it can't be an indigenous society either).