Margaret is recovering well at the Starship children's hospital after surgery last Friday to correct her inherited heart defect.
Karen is stable. Doctors will decide this week whether to do the first of two or three operations spaced over several years to fix her defect, which is more complex.
She would need a high degree of medical follow-up and Starship heart surgeon Kirsten Finucane believes she would be unlikely to receive this in Vanuatu. Without the surgery, she is expected to die within several months.
But Dr Allen is adamant he can provide the follow-up and said the surgery should proceed.
Karen is among six people, mostly children, he has helped come to New Zealand for heart or cancer treatment. It is paid for from public donations, media and service-club fundraising, and New Zealand's Vanuatu medical aid budget.
But Dr Allen already owes Auckland District Health Board $10,000 from a $46,000 heart operation on a Vanuatu boy.
If the trust cannot afford all of the estimated $35,000 to $40,000 cost of Margaret's treatment, he has underwritten the rest and offered the same for Karen's surgery, expected to cost at least $70,000.
His overdraft is already $16,000 and he earns only $15,000 a year from Vanuatu's Ministry of Health as the sole doctor for 35,000 people on the 16 islands of Malampa province.
He said he would resign and return to New Zealand for a higher salary to pay for the girls' treatment if necessary.
Dr Allen originally wanted to be a missionary doctor. He gave up religion while at university, but retained a zeal for serving the poor. After qualifying as a GP he worked in Botswana, Swaziland and South Africa. He returned to New Zealand and practised for several years in rural areas then headed to Romania, Ukraine, Bosnia and Albania.
Another New Zealand stint followed before he went to Vanuatu in 2001.
"I just think we're here to do the best we can. I've had everything I needed in life; now it's time to give back to the world. I reap so many rewards in giving back, as well."
He describes his Vanuatu work as "challenging" and says too many people die of easily treatable conditions, especially diarrhoea, often because they cannot afford the boat trip to see him.
He hopes the helicopter will make a big difference by allowing him to quickly reach clinics on remote islands which now take him away from his base at the 58-bed Norsup Hospital on Malekula Island for up to six days because he has to travel by plane and boat.
Those wishing to make a donation towards helping pay for the surgery can do so into the Operation Vanuatu Charitable Trust at their local Westpac branch.
Doctors in dilemma over baby's heart surgery
Herald Feature: Health system