Sarah Brennan, 36, from Llantwit Major, Vale of Glamorgan, gave birth to Eryn in September.
She was born seven weeks premature, weighing 3lb 11oz (1.7kg).
Mrs Brennan and her husband Mark have thanked the special care baby unit (SCBU) at Princess of Wales Hospital in Bridgend, where Eryn spent three weeks.
The couple had just been placed on the IVF waiting list when they found out Mrs Brennan was pregnant.
But her waters broke in her 29th week of pregnancy and she spent two weeks being closely monitored in Singleton Hospital, Swansea.
She returned home but had an emergency Caesarean on 30 September at Princess of Wales Hospital as the baby was in a breech position.
Mrs Brennan, who works as a project manager at RAF St Athan, said: "Although Eryn was born nearly two months early she is a right little bouncer now.
"You would never think she was a premature baby."
Mrs Brennan's employer has donated Â£500 to the SCBU.
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