I think that at 13 your daughter is probably old enough that you should talk to her about it. Read up on the reasoning behind the Church not being allowed to ordain women, and I would also read JPIIs Mulieris Dignitatem (you can find it online). Then I would talk to her, explain your concerns, and see if you can convince her. The thing you want to avoid is her leaving the Church in 8 or 10 years because it is “sexist” for not ordaining women. Now is a good time to discuss with her the Church’s very correct teaching that although men and women are 100% equal in dignity, that does not mean that they are equivalent.
In our diocese, the bishop has left it up to the pastors whether female altar servers are allowed in a parish and our pastor doesn’t allow them. We always have lots of altar servers. I have never seen a shortage. My previous parish did allow female altar servers, and was about twice as big as my current parish, but at least once a month, there would be an announcement, “Are there any trained altar servers in the congregation? We need at least one more…” It’s just anecdotal, but what other kind of evidence could there be that wasn’t self-report data (and therefore inherently unreliable)?
It is foolish not to realize that the dynamic will be very different when both female and male altar servers are at the same Mass. Whether or not there are objections on the part of the male servers, or whether or not there is giggling, there is distraction. The boys and girls will not be paying as much attention to the Mass in a mixed group as they would be paying in a single-gender group, whether they are at the cooties stage or the crush stage.
In addition, it is possible that some boys like the idea of being altar servers partly because it is something they can do and girls cannot. There are VERY few such things left in society–there are many more things that girls can do and boys cannot. E.g. many times, girls can join the boys’ sports teams, but not vice versa, and there are more women-only colleges and universities than men-only ones.
However you need to keep in mind that removing your daughter from the altar server program is not going to actually fix any of the problems. There will still be other female altar servers, so the distractions and so forth will still be there. So if you can’t talk your daughter into leaving the program on her own, I would let her stay in. I can (just) remember being 13, and I think that if my mother had treated me that way (tried to pursuade me to do something but accepted my decision) about something it would have made our relationship much better.
You might see if she would be interested in putting in some practice to be a Lector instead, if your parish would allow someone so young to do it.
God bless!
–Jen