He revealed during a Twitter question and answer session that Amelia was an early bird, waking her Dad up at 6am.
Singer Pete suggested to fans that Amelia usually wakes up even earlier, which means he has to reach for his beloved coffee.
He tweeted: ‘I thought 6 was a lie in today. I always do early morns. And I love it..... After 2 espresso.’
Peter revealed in an interview with a UK gossip magazine that he tends to do the early mornings so fiancée Emily can catch up on sleep.
He confirmed that this is still the case, writing: ‘A asleep on me downstairs and E asleep upstairs haha.’
The 40-year-old tweeted more about his early starts, writing: ‘Been up with little A since 6 but she is awesome :)'
He continued gushing about his new addition: ‘She is so bloody cute honestly. She is awesome.’
He also talked about his daughter Princess’ enthusiasm over her new little sister.
He wrote: ‘Bista is just a little obsessed with her. It's great to watch.’
Pete and 23-year-old fiancé Emily MacDonagh welcomed baby Amelia into the world in January, revealing the traditional name 4 weeks later.