I traveled solo and there was one other solo woman and a few women traveling together, (mother and daughter, two close friends). You'll get to know people quickly and will have people to eat with if you want.
Eating alone does not bother me and I like getting out and exploring on my own and it's safe to do that in all the cities on the tour and there are numerous dining options. There were several group meals, which tend to be long with more food than I need, so I was happy to find places to eat on my own when meals were not included. I also like to get out and walk around after a long day on the bus.
In Sydney I walked from the hotel to China Town and got delicious take out, and sat on a bench watching the crowds go by. In Cairns I walked down the street to the night market and got noodles with shrimp and saw several people from the group wandering around the market. The night before we left Sydney I got take out from the hotel restaurant and ate in my room while enjoying a wonderful view of the city. The first night in Fiji I went to the lagoon side restaurant and had a wonderful grilled fish dinner. The last night in Fiji (packing night) I got room service and ate outside on the patio and listened to the waves lapping over the reef. One lunch in Fiji I joined five or six people at the lagoon restaurant.
I had a wonderful vegetarian sandwich for lunch at the cafe at the arts center in Christchurch. You won't be going there but I'm sure you'll find something in Rotarua. In Queenstown a few people were going for pizza, but I don't eat it, so found a vegetarian restaurant and had a great salad.
You don't need a backpack; only one person in our full group used a backpack, use whatever you usually do when traveling. You will need a rainjacket, the one you have sounds fine. I don't think you need a vest with pockets. I have a Columbia cotton vest that I sometimes use and keep my money in the chest pocket and my small camera in another pocket -- I like it for times that I don't want to carry a purse but it certainly isn't essential.
Sorry this ran so long, I just wanted to let you know that there are many options for meals.
You have a great trip ahead, just go and enjoy.