Bushwalk Australia

I have a flexible work schedule now, and would like to walk the OLT this season, and combine it with a stay in Hobart with my sister and her family and my Mum. I may combine it with some Tassie veterinary locum work (apparently they find it hard to get locums)
Anyway, just asking which is the most favorable month to walk this track? I'll be going solo, unless anyone wants to make arrangements to join up, but I have suitable gear, PLB, am reasonably fit but only have experience in short multiday walks, nothing as long as this.
I've heard Oct is still very wet. Late Dec/Jan is out as I'll be in Patagonia with hubby. Nov? Feb? March?
Thanks for any suggestions.

November or March. I've had the most stunning walking in early March the wind has usually dropped but the days are still warm(ish).

If you get in before 31st September, you dont have to pay the $200 per person fee, but the weather in September is still a bit random. I suggest October or November, but always be prepared for anything.

Usually the most settled weather is in Feb/March.