Abbey gave birth to the couples first child on 15 March.
The pair have named their baby girl, who weighed in at seven pounds nine ounces, Sophia Ruby.
A source confirmed the news, saying:
"Mother and daughter are doing brilliantly.
"Abbey and Peter are over the moon. They are completely in love with her."
Twenty-five-year-old Abbey has said previously that she thought she was having a boy.
She told This Morning hosts Eamonn Holmes and Ruth Langsford:
"I think it's a boy from looking at the scans...it's too boisterous to be a girl!"
The rounded sleeping capsules send guests drifting into ocean before arriving on desert island by morning.
Sitting on the saddle activates the part of the brain responsible for learning, a study has claimed.
Scientists are appealing for more people to donate their brains for research after they die.
Life on Earth may have arrived from Mars on an asteroid, scientists have claimed.
Lunar mission scheduled at the end of 2017 could find out if beer can be brewed on the moon.
A bottle used to teach children how far litter can travel ended up on Scottish beach after 8,700-mile journey.
Confused Apple customers are finding coins in their MacBooks.
x Share us on Facebook