Hi!
I love Australia in the summer time, but it does get very hot around January/February and if you're not used to it, it could affect your enjoyment! I live in sydney and temperatures here in summer often get to around 30 C (86 F) or higher.
New Zealand's summer isn't as long and hot as ours, so maybe if you're keen to leave sooner rather than later, I'd do New Zealand first, then Australia, then SE asia.
this is a good guide on NZ's weather, from the look of it the summer there doesn't get that hot at all! I think March would be a great time to hit australia, it's still very summery but the unbearable heat of jan/feb is usually gone by then (sydney temps are probably around 26 C - 78F) I'd start off on the east coast before doing any outback/northern territory exploring. In those places, it's hot all year around but the temperatures do dip a few degrees in winter (june, july, august) so the later you go, the better.
Also, with ten weeks, you have plenty of time so my main advice for travelling in summer would be to take it slowly - allow time for lounging around under big shady trees in the park, plan any indoor activities between 11am-3pm so you're out of the harshest sun. and for god's sake, DO NOT do what all the other tourists do and spend all of your first day here lying on bondi beach trying to get a tan! it won't work and you'll be red and sore for the rest of your trip. Aussie beaches are best enjoyed in the morning (and anyway, that's when all the hot local surfers guys & girls are there
)
let me know if you have any other questions!