It isn't unusual, but I would encourage you NOT to breed them because she is waaaaaaay too young. A year tops, is the potential breeding period otherwise, you risk your female becoming eggbound because their bodies are not fully developed and are smaller, or other reproductive issues, and quite possibly, and I am not going to lie to you, a very early death.
My little Nutmeg was being wooed by my Zucchini 'cause they loved each other so much, and it was approximately less than a year before they started breeding. I believe this was a mistake and really didn't ask for that to happen, but Zucchi had other ideas, and well, Nutmeg was receptive to it. You just can't break up a good thing but if I could do things differently, I would have NEVER had them co-mingle until a year's time.
That, of course, doesn't mean health problems can't happen with one's budgie, just that it is recommended not to breed until the female is a year or more old. Had I done things differently, I may have prevented future problems with Nutmeg and she might still be with me today. After a few clutches, she started to go down hill and had one siamese egg partial egg binding experience and then started to develop an ovarian issue.
So, even though budgies in the wild are sexually mature from 16 weeks on doesn't mean your caged birds should be. It's fine if they develop a relationship, but watch that birdie mounting business. Try to discourage it, but once it happens, it's very hard to stop them from 'engaging' when your back is turned and you aren't looking.
Note: Just for the record, I am not super experienced in breeding budgies so I look forward to anyone who is adding some more information.