You've gotten good advice so far...I think your first logical stop would be her bank or credit union. If she has had an account relationship with them and kept her nose clean (no or maybe only one bounced check or overdraft), they would likely give her a starter card. With no baddies on her credit report, it won't take long for her FICO to rise. As soon as she is able (probably six months) she should get another couple of credit cards, always paying on time and keeping her balance below 10% of the credit limit.
You'll be amazed how fast her credit score starts rising by autumn. I have a friend of mine whose FICO is around 690, and she's only had credit a year. By the end of the year, she'll be around 720 and able to get approved for just about any reasonable credit offer. No reason your daughter can't do the same.