The UA website clearly asks for the number of passengers and has a link marked "children" right next to it. If you click on the link, you get a box calling for the number of adults, children and infants (all with age definitions clearly marked).

Whether there is a children's fare on OP's specific route and fare bucket is another matter. If the tickets price at twice that of the adult fare, it's worth a call to UA to make certain that this is not a glitch.