Hello,
It's great to know we have another young person entering this maddeningly addictive sport--and a female person to boot

It's wonderful as well to hear from a parent who is concerned about and involved in her childs activities, kudos to you for that
Now to answer your question. The generally accepted wisdom around my club is usually that children should start at around 8yrs old as well. The reasoning I heard behind this is that it's an issue of maturity, both physical and mental. Fencing is a sport that requires a lot of coordination, eye-hand and otherwise. Generally kids coordination doesn't completely develop until they're around eight--heaven knows sometimes I think that at twenty something my coordination still hasn't reached the proper level--but as with everything, there's always exceptions. If your daughter isn't feeling frustrated, then it's probably not a problem. The other concern is that fencing requires some pretty complex thinking sometimes--it's called physical chess for a reason--again it's generally accepted that kids aren't fully capable of complex, abstract thought until they're a bit older, but again to everything there's an exception. As far as size, being small isn't necessarily a disadvantage--granted it's unnerving if you're an adult fencing this tiny little person--the good thing about fencing is that people with different physiques and strengths can create a "game" that will be sucessful. Around my club we've had some kids who were pretty small who have become pretty competent fencers.
Anyway, you say that your daughter is enjoying this and imho as neither a coach or a parent if she's having fun, let her do it. While perhaps your local fencing center may not let her participate, I can't see it happening. I would think that if she is enthusiastic about it and really wants to do it, they would be more than happy to have her, especially since whoever gave her the first lesson didn't seem to have a problem with it. Also, check for multiple centers in your area by searching the club section on this site. It may be that if one club won't let her join, another one will.
That's my unprofessional opinion on the subject anyway.