There's some merit to your concern; girls who are "into you" will be all over you. IM, e-mail, text messages, gifts, she tries her hardest to prevent you from forgetting about her. She wants to see you again as soon as possible.
BUT, it's possible you have a mentally stable and "enlightened" girl, which is infinitely better than the former I just described. There's a lot of context you're leaving out. How long have you two been together? How far do you live from each other? Is she heavily involved in work/school/other activities?
Make sure every time you meet is positive and quality time. One way to check if she's into you: Cancel a date. If she promptly suggests a new time or day, she cares about meeting you enough to set up a new plan on her own. If she's okay with going another week without seeing you, that's a red flag.