Quotes from interviews
[After Emily's father operated on him] Mysterious Girl singer Peter continued: "We became friends and I met the family, and for two years we were all friends - Emily's family and my family.
"I think it was two years later we were all in Zanzibar. I'd gone on a holiday with them because they work with the health care system out there.
"And I remember they all walked together holding hands. It's such a lovely thing. I used to see them together holding hands [Skipped a chunk]
....On one side I'm holding Emily's hand, and on the other side I'm holding her father's arm.
"And I was getting tingly feelings on one side of my body, and on the other side of my body I was so nervous because I didn't know what I was feeling.
"And I thought 'Oh, no, I've got feelings for Emily - what do I say?'
So he decides to approach her father and tells him he has feelings for Emily and the Father gives permission - you could argue the father didn't have much choice really, but isn't that pretty much the case these days anyway? - but the father does say he felt he suspected there was chemistry between the two of them and gives permission.
I'm assuming by now Emily is 22 possibly going on 23
There's a couple ways of looking at it. PA meets the surgeon father who operates on him. Emily as per PP above, finds out father has contact with PA and asks to meet him. Father introduces her. Peter Andre takes a shine to Emily and stays in touch with the surgeon ostensibly with the purpose of continuing to be in her orbit but possibly styling it as some higher purpose.
Or
Peter Andre meeting Emily was totally sensitive to her younger age and so held back from making a bold move, instead getting to know her through interacting with her family, and introducing her family to his. He realises this would be serious and not a mere fling. He observes her character and her family values and likes what he sees. He is totally respectful in his interactions with her and respectfully seeks her father's approval before dating her.
It does say Junior and Princess are still quite young children when they are introduced.
I personally would not like my daughter to be a step mother at such a young age and for her first serious relationship, but life isn't always neat and tidy and she is immensely sensible and her based family values have translated well to being a very good SM.
I am not sure if she became a practicing GP before their first child was born. It's absolutely ages ago but I seem to recall her taking some time out but that could have been afterwards.