First time OLT in Sept?

Hi all We are contemplating the overland track the week of 17 Sept, at least we were until I started trawling these forums! We are Queenslanders with minimal snow experience and we'll have our 10 yo son with us. We'll have all the cold weather and wet gear etc, but I'm worried now about heavy snow. It seems more than likely there'll still be significant amounts of it about at that time, is that right? We are not worried about cold or bad weather but don't have snowshoes or experience using them. The other sticking point is that as travellers to Tas our schedule will be pretty well locked in with next to no wriggle room to change our plans...
I think I've just answered my own question but any thoughts appreciated, especially from others who've been in the same boat and gone ahead - worth it or bail and go in height of summer?
I think I've just answered my own question but any thoughts appreciated, especially from others who've been in the same boat and gone ahead - worth it or bail and go in height of summer?