There should be no problems with making a dash into the dairy. A few months ago, we asked Henry if we could, and he was fine with it. I can't remember the exact time, but it would have been early afternoon.
In our opinion, the store wasn't particularly well stocked and quite expensive.
All we ended up buying was some drinks (cola, tonic water, Just Juice and bottled water).
The cola was awful. They didn't have coca cola, just one of those cheap, sugary brands that goes flat really quickly. For our next trip, we'll either see what they stock at the airport, or buy from the resorts mini-bar (which was reasonably priced).
As you know, the water at the resort is safe to drink. But we were grateful for the bottled water on morning excursions. But again, we could have bought that from the airport.
As for snacks, we made room in our suitcases for 3 packets of biscuits and just declared them once we arrived in Fiji. Over 9 days, between 3 adults and one child, we didn't finish the biscuits. The meals were always so large.
Lastly, just a quick tip. Buy any magazines you might want, in NZ before you leave. I almost had a small heart attack when I saw what they try to charge for magazines in the Fiji airport.