It really depends on the cat(s). Generally, younger cats adapt more quickly to being adopted out, but older cats can adapt fine as well. If they're bonded, having the cat(s) they're bonded with adopted out with them to a new home can help them feel more at ease than going alone. Older cats who have lived in a home for a long time will be used to the home they know, so it's a bigger change for them. With the new owner's patience, they'll eventually start to feel more at home there and get more comfortable with new people and new sights, smells, etc.
It depends how long the girl is gone. Some cats are more aloof, so they don't always need someone to be with, whereas other cats are very social and experience anxiety when their people are gone. As long as she can provide quality time for the cat when she is home and the cat doesn't feel stressed being alone, it should do fine. Also consider how much cats sleep - if she is gone to class during a large part of the day, her cat will probably spend quite a bit of time napping, and can wake up to enjoy her company in the evenings when most cats are more active.
I would argue there is no "perfect age". I know some people prefer to adopt young cats, like under 6 months or under a year old so they can "train" them for the rules of the house and such since they're a bit more malleable (plus, their 'baby cuteness' is very endearing). My boyfriend used to say he didn't want a cat over a year old because they could have bad habits from their previous home, but I don't believe that. In most cases, you can reinforce the behaviour you want in a cat of any age.