But despite his packed schedule, we managed to nab Peter for a quick chat about breastfeeding, bridesmaids and bad jokes.
Congratulations on the birth of your daughter Amelia and your engagement to Emily MacDonagh. January has certainly been an eventful month for you!
Thank you! It's very strange how it all happened in the month of January, especially as it's been such a huge contrast to last January, which was one of the worst months of my family's lives, as we'd just lost my brother in December.
Even though everything's still raw in that department, so much good stuff has happened with the engagement and the new baby this year.
Who picked the name Amelia? You or Emily?
Well, it's really strange because the first person to mention the name Amelia to me months ago was Emily. And I said, oh I love Amelia.
Then all these other names were thrown in, but I kept coming back to Amelia, and every time it was brought up I thought actually I love that.
Eventually we decided on two names: Isabella and Amelia. Then me, Junior, Pringles [Peter's nickname for Princess] and Em sat down and decided to vote for our favourite. Out of the four of us, three picked Amelia.
Who didn't vote for Amelia?
Junior wasn't 100 per cent convinced with either name. I did get him and Princess involved in picking names, but then I did say as a joke – well, it was a joke but it's got truth to it: "I am asking two children who named our pug Porridge, so... maybe not the best idea!" But Bista [another of Peter's nicknames for Princess] absolutely loved the name Amelia. She's had a lot of say in this.
She even had a say over if it was a boy or a girl. She said, 'I'm telling you if it's not a girl, I'm not interested!' So she got what she asked for.
Have you chosen any middle names for Amelia yet?
They're a work in progress, but we'll be keeping them traditional, and maybe use family members' names.
Who does Amelia look like? You or Emily?
Thankfully she looks more like Emily! She has Emily's eyes, but she has my nose and my dimples. I'm glad she's got my dimples - but not so glad she's got my nose!
How's Emily finding being a new mum?
She's fantastic. She's awesome, a great mum and she's taken to breastfeeding really well. Now I want to make it clear that not every woman can breastfeed and there's nothing wrong with not breastfeeding. But clearly for the people that do, there are some huge benefits and for the first time I've experienced seeing it happen and it's just incredible. But every experience you have with a child is hugely special and they are just as special as each other. It's just different.
Do you think Emily's medical training has made her calmer as a new mother or is she a worrier?
One hundred per cent it's made her calmer. I've never been able to quite believe how calm she is. How sensible she is. She's a logical thinker.
You were there at the birth?
How did you feel?
I was scared on the way to the hospital, because Emily went into labour while we were in the car and we still had another two hours to drive.
It was scary. Every time we went past a city we didn't know whether we should just veer off there. We passed Reading, then Swindon, then Bristol and each time we didn't know what we should do, but we made it in the end and once we got to the hospital I felt much calmer!
Do you think you and Emily will have more children?
I don't know. I know that we probably want to be married before we have any more, so it won't be for at least a couple of years yet.
Getting married is not an 'if' anymore, that's the good thing. Although it never was an 'if' for me. But I think we'll wait for a couple of years, so Emily can finish her degree and get settled into a job.
How did Junior and Princess react when you told them you were getting married?
Bista turned round and went, "Er, hello! I already knew that. I've seen the ring on her finger for the last few weeks."
Because I proposed on New Year's Eve and we wanted to wait for the right moment to tell them.
I was like "How did you...? You are so intelligent." And she went, "I know!" She's a very bright girl. I love her so much, she's incredible.
Junior was so happy too, but he was like, "Really?!'"He hadn't noticed the ring – like a typical guy!
Will Princess be a bridesmaid?
I think that would be without question. The wedding will be a beautiful family affair when it happens.
And because we're waiting a few years, Amelia will be old enough to walk down the aisle with us. Just thinking about that makes me happy. I know it's a way in the future, but it's great!
What about Junior, will he want to be involved in the ceremony, or does he not like the attention?
Junior loves the attention! I don't know how he'll be involved, I haven't thought about it, but he may well be the entertainment - he loves to perform, that's for sure.
Are Princess and Junior enjoying being older siblings?So much! To me they look like teenagers now the way they act towards the baby. Sometimes I hear them going, "OK darling, that's no problem, don't worry." They've both really matured.
As a father did you enjoy being involved with a movie about a father and son relationship?
There is so much similarity between Peabody and Sherman, and me and Junior.
OK, I'm not a genius like Mr Peabody, but I am very bad at telling jokes like him. There's this bit in the film when the girl says "We're in the Nile." And Mr Peabody says, "No, you're in denial" - which is exactly the kind of terrible joke I would tell.
So you're guilty of sometimes telling jokes that don't hit the mark?
No, not sometimes – they never hit the mark! I think it's important to be consistent. If you're going to tell bad jokes, at least be consistent with them, because then they become funny BECAUSE they're so bad.
What joke have you told Junior and Princess recently that made them groan?
They asked me about nephews and nieces and that sort of family stuff, and I turned round and said in a Greek accent, "This is the niece and this is the elbow." While pointing to my niece and then pointing to my elbow.
And they didn't get it. They were like "What? ... it's terrible".
But seriously, it's amazing how well the Mr Peabody & Sherman movie ties in with my life. The bond between Mr Peabody and Sherman is just incredible – and that's so true for me and Junior.
And now whenever you look back at it, or listen to the song you recorded for the film you'll be reminded of the time Amelia was born.
I'd never quite thought of that, but you're absolutely right. The video for Kids will be tied to everything that's happened this January. Let's just hope Amelia likes it!
Peter Andre's new song 'Kid' is the UK's official track for the new DreamWorks Animation MR PEABODY & SHERMAN, in cinemas from 7 February.
More on Parentdish: