It's my first year as a K-8 teacher's aide, and the administration wants me to transfer to a new high school next year. Should I ask for a raise specifically since I'll be working with teenagers?

Along with the other quite valid answers, I would add that you might be justified to ask for a raise either based on your perceived value (since they are asking you to move) or to offset the disincentive of moving insofar as it means adjusting to some change. To specifically ask based on the fact that you would be working with older children implies (strongly) that you don't feel able to do that.  By definition, this would be an excellent reason for your administrators to doubt your ability as well. In either case - I would recommend pegging your salary request to something other than the age difference.

In most US K-12 school districts with union representation the collective bargaining agreement (contract between the teachers and the school) uses the same wage scale for ALL teachers in ALL 13 grade levels and for ALL subjects. Teacher aides, who are uncertified teachers, earn less than teachers but also the same amount for all grades. These contracts usually feature automatic raises based on the number of years employed. Since you work in a charter school, which are usually not unionized, this model is not in effect. Since the consensus among the vast majority of teachers (most are unionized) is that there is no need to differentiate pay according to grade level taught I would cue from that and ask for a raise based on your perception that they value and need your proven skills and personality at the new school. After a year of employment they know who you are and they want you to stay. Who you teach is not the issue - the value you bring to the school is.