That was confirmed on Thursday when Pee-wee was seen taking milk from its adopted mother.
A fellow crew member on the Fullers GreatSights Bay of Islands vessel Tangaroa, Lawrence Hamilton, photographed the calf swimming upside-down and suckling from Kiwi off Onewhero Bay.
"It's just so unusual. The crew are ecstatic," Ms Halliday said.
It was especially heart-warming because Kiwi had become stranded at Aroha Island, in the Kerikeri Inlet, five years ago.
She was refloated but her calf at the time, named Squirt, was never seen again. It was feared Squirt had been eaten by orca while its mother was stuck on the mudbank.
As far as Ms Halliday knew, Kiwi had not had another calf since then, but she was producing milk now.
"There's so many things these guys are capable of doing. They may be able to switch on lactation on demand."
Common and bottlenose dolphins grew at different rates so it would be interesting to see whether Pee-wee adapted to the ways of its new hosts or followed its instincts.
The larger bottlenose dolphins relied on their mothers for 3-4 years, only reaching sexual maturity around the age of 6. Common dolphins grew faster and matured earlier.
It was not known why a dolphin would adopt a calf of another species but Ms Halliday put it down to the large-brained, social creatures not wanting an orphaned dolphin to suffer. It was not clear how much the dolphins themselves distinguished between species.
Common dolphins grow to about 2.5m and are found worldwide, hence their name. They typically work together to round up schools of pilchards and mackerel. Bottlenose dolphins grow to about 3m and are more likely to venture into estuaries hunting for flounder, mullet and kahawai.
Pee-wee's gender is not yet known.