Dr Fiona Agnew, 38, suffered a "sudden and unexpected death" at the Forth Valley Hospital less than 24 hours after the delivery of her second child, Isla Elspeth.
A funeral will be held for mother and daughter on Friday this week in Edinburgh, where the GP lived with her partner, Craig Stobo, and young son Robert.
Mr Stobo, a senior manager at PricewaterhouseCoopers, yesterday declined to speak about the double tragedy.
Dr Agnew was originally from Stenhousemuir, Forth Valley, where her parents, Douglas and Eslpeth still live, and worked as a doctor at a GP surgery in Bo'ness. She has two brothers, twins Colin and Murray, 35.
The family are due to set up the Fiona Agnew Memorial Trust to fund research into hospital superinfections following her death. However, it is understood Dr Agnew, who died on August 26, did not lose her life to such a condition.
A spokeswoman for the Forth Valley NHS Trust said: "Friends of the family have spoken of their shock on learning about the deaths of mother and child.
Irene Rodger, a neighbour of her parents, said: "I've known the family for about 40 years.Fiona has been away from here for a while.
"I've not seen her or her family for a wee while. They lived in Edinburgh and were busy with work. I only actually found out about this myself yesterday and I'm really quite shocked with what's happened.
"They're a lovely family, the children are the same age as mine and they used to play with them when they were younger. She was always a happy girl, just a lovely person, it's hard to take in."
A spokesman for PricewaterhouseCoopers confirmed Mr Stobo would soon be establishing the trust in memory of his wife. A funeral service for Dr Agnew will be held at St Stephen's Church, Comely Bank, Edinburgh on Friday at 11.30am with the service followed by a private committal at Dean Cemetery in Edinburgh.
The baby girl will earlier have been laid to rest in a private ceremony for family only. The family have requested family flowers only and any donations to be made to the trust.
A spokeswoman for NHS Forth Valley said an internal review will be held.
She added: "If there's any kind of maternal, sudden death a review is carried out as a matter of course."
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