The boxer "has always wanted to be a dad," Hayden Panettiere tells PEOPLE. "I think at some point he might have started thinking he wasn't ever going to be and then he was. He is just so over the moon."
Klitschko is already a very hands-on father. "I'm lucky if I can get my hands on the kid. He's like, 'No, no, I got her.' Which is exactly what I thought he would be like. Forget it, he's done," the Nashville star jokes.
As for wedding plans, "I'm not putting a time frame on anything. We don't live like that," says the actress. "We've got this little bundle and we are happy to have her occupy our time. Besides, I've got to wait until she's flower girl age, or at least can crawl down the aisle!"
Kaya "is the wildest combination" of the couple, Panettiere says. "To look at Wlad and me, you go, 'God knows what that child is going to look like!' You don't know if they're going to be tiny or massive. But you can see both of us in her."