Is it fair for a girl to ask for committment after 7 months of seeing eachother?

What level of commitment are we talking about here? Are you referring to becoming exclusive, are we talking marriage? If you care for this girl then let her know you want to become exclusive that means not dating others. Just tell her you want her to be your girlfriend and that you don't want to be with anyone else. If she's already itching for marriage then I would tell you to steer clear because you don't sound ready for that at all.