I know on Emirates the flights increase after December 9th. You’d be going the other way (around the world!) but that’s a rough idea.
It will hot after Christmas in January too but that’s the school holidays. I’d go in October/November rather than actual summer. You might think you want it hot but it can be very unpleasant and you can’t do things if it’s too hot.
Hopefully staying with her most of the trip. February next year would be doable. We can both cope with heat. I’ve spent many trips in Vegas and LA when it has been upper 30’s so I don’t mind that at all.
Minimum we would go for is two weeks. Possibly we could stretch to a third depending on work schedules.
It’s only an hour’s flight (v close in Australia terms) from Melbourne to Tasmania, which has some stunning scenery (eg wineglass bay), history (Port Arthur) and wildlife (devils!). I was glad we made the detour when we visited.
We have just had a three week stay in Melbourne over Christmas. We booked it last April. We went via Dubai and on both journeys were in Dubai for under 2 hours. When pricing flights the prices dropped considerably if traveling from Christmas Day onwards. The 12 apostles are worth a visit. We stayed in colac for four nights in an Airbnb. And also 4 nights in a city centre hotel. The prices of both for the time of year was quite reasonable
Definitely avoid Christmas and New Year. Not necessarily good advice. We usually fly out on Christmas Eve from Manchester and arrive in Melbourne on Christmas day. Flight prices are really cheap at this time! New Year's Eve in the city is good fun! Admittedly everyone won't want to fly then but I'm happy to for good prices!
I normally book my flight to Taz when I'm in Melbourne. If you go to Taz go to the MONA, its bonkers! Back in Melbourne, the city is good, do the Ocean Road over a couple of days to enjoy the sights. Take the cable car at Arthur's seat. The Mornington peninsula is lovely. I can't wait for my next Melbourne trip!