North West Peed on Kanye West During Vogue Shoot, Kim Kardashian Felt Like ...

Photographed by Annie Leibovitz

Being in isn't as glamorous as it looks.

Kim Kardashian spoke about sharing the cover with fiancé on NBC's Late Night Tuesday, where she admitted that her 9-month-old daughter accidentally urinated on her dad during the shoot.

After host Seth Meyers showed a picture of the future spouses and lounging on a couch, Kardashian laughed and said, 'North peed on him right at that moment and he was trying to tell me and I couldn't really hear him. I had to get up and clean her off, clean him off. It's a good memory.'

Though not everyone is happy about the cover, Kardashian is elated. 'To be in this same name as so many amazing people that have been on the cover is such an honor, to have Anna Wintour pick us. I know that it's the first of a lot. They were telling us that Kanye's the first rapper to be on, I'm the first reality person to be on, and the first interracial couple. So all of these just mean so much to Kanye and I. Every girl grows up dreaming that they can be on the cover of Vogue,' she said. 'And I collected vintage Vogue s forever. It's just honestly the biggest dream come true and I'm just so honored to be on the cover.'

NEWS: How Kim Kardashian kept her Vogue cover a secret from her sisters

Shooting with Annie Leibovitz and working with Vogue's Hamish Bowles and Grace Coddington made Kardashian feel like Sarah Jessica Parker's most famous (and fabulous) character.'Honestly, I felt like the real-life Carrie Bradshaw. It was like the Sex and the City moment where you're doing a shoot for Vogue andtrying on wedding gowns,' she said, referring to a memorable montage in the 2008 movie.

She continued, 'I had to fly to London to meet with Sarah Burton [from Alexander McQueen]. That was a top-secret mission in itself, because I landed and all the paparazzi were there. I had to figure out how to get away from them. I need to get into this office without anyone seeing me, because if it leaked out that we really shot this-I didn't even think the cover was an option, but it definitely would be out of the cards for us.'

VIDEO: Kourtney Kardashian weighs in on her sister's Vogue cover

Photographed by Annie Leibovitz

West, 36, is helping Kardashian, 33, plan for their big day. 'He's super creative and I'm so excited that he's really involved in just making sure that it all looks amazing and is amazing. He's kind of like the strength of our relationship,' the bride-to-be said. 'When I'm stressed out he wants to just alleviate that stress. So even if it's something that he's not really into, he'll figure it out just to help me not be so stressed out.' One detail is in West's complete control: 'I'm leaving all the music up to him!' she said.

Living with Kris Jenner as they gear up for their nuptials isn't always easy. 'We were supposed to move in just for a couple months and it's been almost a year. We're building a house and it keeps getting delayed and delayed,' Kardashian explained. They often visit Paris because it can be 'really overwhelming' for West to be around so much female energy 'at times,' his love said. 'I think he does the best that he could and he's amazing, and my whole family loves him and he loves them. It's great.'

PHOTOS: North West's cutest baby album

Photographed by Annie Leibovitz

Contrary to reports, she has no plans to quit Keeping Up With the Kardashians after tying the knot. 'It is a lot of work. After doing it for this long I definitely have a lot of respect for different people in the same field. I love my job and being on the show,' Kardashian said. 'I think one of the most rewarding things was our lighting guy last week, his name is Landon, he gave me a keychain and he said, 'Here, I got this for you. I've worked for you on your show for eight years and you have created jobs for all of us to where I've now bought myself a home for me and my family.' It was just a really cool moment.'

Meyers then joked, 'And then were you like, 'Can me and Kanye stay there?''

Kardashian laughed and replied, 'That's what I should have asked him!'

(E! and Late Night are both part of the NBCUniversal family.)

PHOTOS: Celebrity couples on magazine covers