It's right. I remember that she was yours.

[Actually, Ziva's Pokemon are part of the reason that Carmen and Hiccup are friends in the first place. Go figure.]

It's better safe than sorry. Some people do, and others don't seem to; I think it has something to do with whether you're a registered breeder or not. Either way, I wouldn't advise trying to fly until you have both. I discovered that one the hard way once.