I took the trip a couple of years ago so I don't remember how many meals were not included. I recall three at the resort in Fiji, two at the lagoon restaurant and one room service the night before we left. All three were charged to my room and I paid with my credit card before we left. I also got two heavenly massages at Shangra La, also on the credit card.
I ate in China Town in Sydney, fun and not expensive ($10-15) and at one of the hotel's restaurants, so may have used my credit card there. In Cairns, I had one very good dinner at Rydges (credit card) and walked with some others from the group to the night market and got shrimp at the food court, again, not expensive. I had a sandwich for lunch at one of the airports, probably less than $10.
There are several reasonable restaurants in Queenstown, including pizza and other fast food. I remember a good Italian restaurant and Ithink my dinner was less than $20.
You'll need cash for tips for the bus drivers. If you watch them loading and unloading all the luggage you'll see that they earn their tips.
I don't think I spent more than $20 for any dinner and maybe $10 for lunch, but the exchange rate has probably changed since my trip so you'll need to factor that.
Our PD requested her gratuity in Am dollars so I brought more cash than usual and used my ATM card in all three countries.
It's a wonderful trip, you'll have a great time.