Hmm. Great question. I'd say it depends on the circumstance. Insulated, protected, comfortable, and controlled personal transport vessel of some sort? I'd think so. Anything that requires literally any physical endurance/ training, that'd be a nope.
I don't think its that they are not allowed, just that they are not needed. Space is still at the stage where it is simply to expensive to send people to space unless you get a good deal from doing back, such as a Mission Specialist in space or a Biologist studying onboard the ISS. Children don't posses skills and talents that are necessary in space, besides possibly the greatest drive to do so.
I think children will go to space when we start making spaceflight affordable enough that we can send a 'human experiment' to space, to study growing humans in space. if you grow up in space, will you grow up taller and fatter and spread out because of zero gravity?! Right now, its just not reasonable.
There is also another topic to discuss, procreation in space. Who will be the first person born in space? Perhaps he will be born in the Lunar South Pole or the Martian Dessert? Obviously, a family would not be separated on a colony, but a space station might not have room for children, at least until much later (Deep Space Nine?)