Kim Kardashian and Kanye West 'Both Want More Kids,' Says Source

05/29/2014 at 12:25 PM EDT

First comes baby, then comes marriage, then comes ... another baby carriage?

They have been married for less than a week, but Kim Kardashian and Kanye West are already planning to expand their family.

Parents to 11-month-old daughter North, West, 36, and Kardashian, 33, 'both want more kids,' a source tells PEOPLE.

'Kanye would have already been trying for another, but Kim just wanted to get back to feeling like herself again first,' says the source. 'But more kids are definitely in the plan.'

Before their Italian wedding extravaganza, the groom revealed the couple's very personal reason for choosing Florence as a backdrop: 'I think that our daughter North was conceived here among the Renaissance masterpieces,' West told Italy's La Nazione.

Fast approaching her first birthday on June 15, North - 'Nori' to her mom and dad - has been in her grandma Kris's care while her parents enjoy a diapers-free honeymoon.

* Reporting by JENNIFER GARCIA

For much more on Kim and Kanye's wedding, including exclusive photos and details about her dress, the guest list, the bridal party and more, pick up this week's issue of PEOPLE, on newsstands Friday All About Kim & Kanye's Lavish Wedding