What's the rush?
Caesar™ doesn't allow children to do whatever they want until they reach a certain level of maturity.
They can't consume alcohol legally, obtain a driver's licence, enter into a contract, obtain a credit card, join the military, get a job, drop out of school, buy firearms, purchase cigarettes, get married, etc.
I like comparing baptism to the stance that the WTS presents regarding marriage, from the old Making Your Family Life Happy book (the gold cover). They recommend that a courtship take place over an extended period of time to allow each person to get to know the other, rather than rushing into a marriage hastily and having regrets later on. They say this because marriage is such a serious commitment, and a vow taken before god.
Why, then, should anyone rush into baptism - particularly if the individual in question is not fully mature (at least not mature enough to get married), if that commitment involves a vow taken before god and is a decision that is considered even more serious than marriage? Jesus was a fully mature adult of 30 years of age. He was certainly old enough to be married, have a livelihood and a trade before his baptism, and before beginning his ministry. He undertook that decision as an adult, having studied under Jewish teachers during his youth. He didn't have his parents coaxing him into it, or wanting to get baptized because all his friends were doing it, the way a lot of young JWs in their teens do. It was HIS decision, as an adult, and nobody else's.
You might, if discussing it privately with your wife, express concern that should either of your children make a poor decision post-baptism that you'd both be required to shun them. Say that you know you've got great kids, but you don't think you could handle it, and you wouldn't want her to experience that pain either. Make it about preventing her from having her heart broken like that. Wonder out loud with her whether it would be better for the children to be a little more mature, a little wiser, so they can make an informed decision from the heart, rather than one that is based on peer/parental pressure. Say you'd hate for them to make a mistake after they got baptized before they were really ready, and end up DFd... and then turn around and say "mom and dad pressured us into it, and now they won't speak to us". It has to be their decision, without any external influence from any source, including yourselves.