As Ms Graham, 27, was being transferred to a waiting air ambulance at Whenuakite School, her little boy was born.
"He was pretty much breathing on his own but he was struggling a bit," she said.
A trainee midwife who had been on the phone preparing Waikato Hospital for the arrival of the pre-term baby was told that Dr Weston just happened to be on holiday at neighbouring Cooks Beach, a 10-minute drive away.
Dr Weston rushed to the scene and took over from a paramedic to stabilise the baby. "Brody was able to breathe adequately for himself," Dr Weston told the Herald. "And he didn't need anything other than a little bit of oxygen support and being kept warm."
Bad weather meant Ms Graham had to travel in a St John Ambulance to Whitianga, 20 minutes away. There, her son was loaded into an incubator in the Westpac Waikato Air Ambulance and flown with a neonatal retrieval team to Waikato's newborn intensive care unit.
Ms Graham and Mr Sheppard followed in their car. The couple also have a daughter, 15-month-old Cassie-Lee, who was born at 37 weeks.
Brody's sudden arrival was no surprise to Ms Graham, who gave birth to a severely premature son, Cody, five years ago. The tiny boy was born at 24 weeks and survived for six months in hospital, where he eventually died of chronic lung disease.
Ms Graham said hearing Brody's first cry was the biggest relief.
"I was just thinking, 'I have to do this all again and am I going to lose this one too?' But once I heard him cry I was relieved. I was like, 'Oh, my God, he's got lungs'."
Ms Graham has a condition which causes her liver to slow during pregnancy and has been told this is the likely cause of the early births.
Dr Weston said some babies born as prematurely as Brody were "in a great deal of strife" but he was not.
"He's a stable baby and he's coming along nicely."
Ms Graham said her son was "doing everything he was meant to be doing", including putting on weight, and would go home on his due date, April 23.