The 'Mysterious Girl' singer and his trainee doctor fiancée Emily welcomed their first child together, Amelia, in January 2014.
Appearing on ITV's This Morning today, he said: "I hope Amelia takes everything after her mother. When she grows up and gets asked, 'What does your mum do and what does your dad do?' She's going to be really proud of mum."
Peter joked on the show he used to be a hypochondriac before meeting Emily, always popping a painkiller for any ailment. "Emily said, 'Do you really need to take that?' She talked me through only taking medicine when you need it. Then I freaked out and thought I should never take it and would get sick. But now I've found a balance."
As well as looking after his baby daughter, the singer is preparing to hit the road in support of his brand new album Big Night. The record was inspired by a visit to New Orleans and a love for artists like Elvis Presley and Stevie Wonder. Among the tracks featured on it is 'Kid', the lead song from DreamWorks' animation Mr Peabody and Sherman.
"We've got a ten piece band that we're taking on the road and the whole album is just blues, jazz, swing and rock and roll," said Peter. "The reason we did this was because I love it, and its the tenth studio album so I wanted to do something I love. It's all live, which was such a good experience."
Peter admitted it will be tricky when he's on tour, particularly as Emily will be busy as well finishing her degree. She's studying to become a doctor.
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Celebrities who welcomed babies in 2014 in pictures:
Copyright: Rex Features WENN/Matthew Taylor/Daniel Deme/Josiah True/Matthre Taylor/Joe
Watch Peter's music video for 'Big Night' below: