A friend and I traveled to Australia and New Zealand independently four times and loved every bit of it. She's gone now, and I'm too old to travel that way. The people are very very nice and welcoming, and there's no language problem. Well, maybe a little bit, but you get used to the slang. Food is great, especially if you're into seafood. If you're a meat eater, the beef and lamb are also good. We both were wine drinkers, and the wine in both countries is excellent. I still prefer Australian and New Zealand wines to Californian and definitely to French.
We always stayed overnight at LAX both ways, since we were starting at Logan Airport in Boston.
The weather in November would correspond to our weather in May, depending on where you are. I swam in Cairns in October one year. But in Queenstown, I needed a fleece jacket with layers underneath.
I advise you to take advantage of all the optionals. After all, when will you be there again? Have a great trip!