no that's something you can do as well.only if they are adults. click on the actions button of the adult dragon of your choice and sometimes(i'm not sure why it doesn't do it all the time) there will be a breed button. click it. and you can choose any of your other dragons, who are of the opposite gender, and have the breed to make an egg. sometimes they won't breed, or will but don't produce an egg, or sometimes produce too many eggs so you have to abandon all but one.

hope that helped!