In the 1800s how long would it take to get from Britain to Hobart, Tasmania?

At least 3 months, possibly as much as four or five months, if the weather was bad on the way and they had to stop for repairs.

By the way, in autumn 1827, one of my relatives carried out a burgary, got caught, and was sent to Tasmania in spring 1828. My guy and yours probably knew each other.

Well, 1827 is before oceanic steam ships so the vessel would have moved under sail power. It certainly would have taken many months. Crossing the Atlantic usually took 6-8 weeks under sail. It is much farther to Tasmania. Getting more specific is difficult, though, because ships would have had to stop at ports to take on more supplies periodically, and those port calls would have added time onto the pure sailing distance. I'd recommend looking between July-September of 1827.

There are some journey times in the documents in the link below. Voyages to South Australia seem to have taken around 75 to 90 days unless there were unusually delays. The early steam ships were not necessarily faster than the best of the sailing ships.