She never texts first, but when I text her she enthusiastically replies. What do I do?

If you hate people who have better things to do than send you mindless texts, then you should definitely dump her.  

Otherwise, why not ASK her?  Tell her that you'd really appreciate it if she'd make an effort to reach out to you.  Then wait and don't text her to see what happens.  Maybe you're just insecure and expect too much. Maybe she isn't much of a texting person.  Maybe she has zero curiosity about you.  Only way to find out is to ask her instead of playing games.

There is no "should".

Like many girls and women, she expects you to take the lead. She is probably in the "reactive" category, so you need to continue to be proactive. 

If i were you i would just stop talking to her and force her to be the one that has to text first!