I have the same habit while texting. But I try not to do it before the first date. My thoughts on double texting are:

1. Before first date try to avoid it
2. It's okay to do it after she does it
3. It's okay to do it once in a while specially if she is showing lots of interest
4. It's somewhat okay to do it if you are handling two threads at once (not the case here I would say)

Overall I don't think it's a huge deal breaker specially when the chick is into you but will make some lose interest