The mother of four-week-old Summah, Rhyannan Bradford, 23, praised the state's health system when Health Minister Daniel Andrew stopped by Summah's humidicrib at Monash Medical Centre last week.

Summah has been nicknamed 'Mummy's little fighter' after she was born premature at 27 weeks on Boxing Day.

Ms Bradford sensed something was amiss when she had sharp chest pains the morning after Christmas. "I didn't want to go to hospital, but something inside me said it was time to go."

She arrived at the hospital at 6.30am and Summah was delivered by caesarean section at 1.46pm.

"We like to think she's a belated Christmas present, the best a parent could ever ask for," Ms Bradford said.

Her unusual name was chosen long before her birth because both parents enjoy summer time.

Summah was originally due in autumn, but Ms Bradford said her birth in December confirmed she had picked the right name.

"All the nurses just love Summah," she said.

"She's very stubborn and she's a little girl who knows what she wants.

"If she's not happy, she'll make sure people know about it."

Ms Bradford said it had been hard watching her daughter live out the first weeks of her life in a hospital cot.

"We don't know when we'll be able to take her home.

"We have our ups and downs but at the end of the day we know she's in the best place for her right now."

She praised the new beds package. "I'm sure that there's going to be many grateful parents and I'm one of them.

"Many people don't realise how often babies can be born early and need hospital care.

"It is so important for us to get funding for hospital beds so our children have a better quality of life."