Peter, 40, spoke about his plans to marry medical student Emily in August, after a number of reports suggested he had already popped the question.
"(The reports) forgot to put the word 'yet' in there," the father-of-three said, in a video entitled The Truth about Emily and marriage. "Without that word 'yet', it caused a commotion.
"When I do do that, it'll be between me and her. She'll be the first to know. I can promise you that."
Last week, Peter took to Twitter to thank his fans for all their well-wishes following the birth of the couple's daughter.
"Btw a massive, massive thank you to everyone who has sent congrats and well wishes," he wrote to his three million followers. "She's such a beaut. Love you all lots."
The Mysterious Girl singer and 24-year-old Emily are yet to release the name of their first child. For the time being though, she has been nicknamed 'Bista's sister', in honour of Pete's older daughter Princess – who is also known as Pringles.
"Pringles is absolutely obsessed with her sister. At this point, we still do not have a name so she’s known as Bista's sister," Pete revealed in a video message on his website.
"The reason we call her Bista is because when (son) Junior was younger, he couldn't call her sister so he called her Bista. So now the new baby's known as Bista's sister. Could be a bit of a tongue twister, that!"
Peter and Emily have previously said that they like traditional names. Ahead of the little girl's arrival, the star revealed, "I like the names Rose, Alexandra and Cleopatra."