This gets into some of what people might consider spoilers - which is always the case when talking about a series that's been around for 50 years - some people may not have seen several years worth.
While I have watched the series since Tom Baker (and Leela) on late night PBS in the eighties, I don't consider myself an expert. I have friends who are though. I didn't follow the rest of the doctors as much but have seen episode from all the incarnations. I watched the American Doctor Who movie when it was on in 1996, and have followed the new series since they brought it back with "Rose" in 2005. I believe that, if you're not going to watch the entire series from the beginning, "Rose" is the best place to start.
It's been announced that the current actor, Matt Smith, is retiring as The Doctor on the long-lived British series Doctor Who. Some of the Internet seems to be upset that the new Doctor will not be played by a female actor. They want to know how they can tell their daughters that she can't be The Doctor but are relegated to being companions as they are female.
Well, if you have watched the series, they have had female Time Lords (Romana) and even male companions (Rory and Adric). "The Doctor" is not really a position but more of a name. It would be like saying you can have a woman be a Green Lantern but not a Hal Jordan.
People say that this answer is a cop out as, since the Time War, there are no more Time Lords. There were no more Daleks at one point due to the Time War - but that didn't last either. The Master, another Time Lord also has made appearances since then. It seems that the Time War wasn't quite as final as we were led to believe.
What to tell your daughter? How about telling her that she cannot become 'the Doctor' as she is already her own person and could no more become 'the Doctor' than she could be you or even her brother. Since neither she, nor you were (probably) born on Gallifrey, she cannot become a Time Lord as she is not already a Time Lord.
If she's more concerned about how she would like to play the Doctor, then she can, all she wants. That's what imagination is for. She could make her own videos and fanfic and be whatever doctor she wants - male or female. She can dress up as her favorite Doctor as much and go to conventions and be appreciated.
My son has dressed up as the Matt Smith Doctor and we have run into at least two other women dressed as the same Doctor, here at ComicCon and at ValleyCon. Besides Fez's being cool, Matt Smith's hair and features seem to lead itself moreso than Christopher Eccleston's did. Laurie Smith has also dressed up as a convincing Tom Baker version Doctor back in the pre-internet eighties.
If she's petulant enough to want to be The Offical Doctor on The Real TV series then you have more important issues to discuss with her - like how the world is inherently unfair and that it incredibly unlikely her, or even her brother will ever play a character that less than 20 professional actors out of a population of several billion have played.