Can I do that? (Legal Advice)

So I have a 4 year old daughter, her father and I are split up and both married to different people. We all live in New Mexico, he lives about 40 minutes away from us but sees her all the time, every other weekend and we split up her school breaks. He pays court ordered child support, but we've never been to court over custody. He's on the birth certificate but I'm the custodial parent. He still has rights and such, of course.

Well, my husband I want to take a trip to Alabama next summer go visit his family. Can I legally take her across state lines? Will I get in trouble? Do I need his permission or something? I just don't want to be accused of kidnapping or something. we'll only be gone about a week, but I don't want to get involved in any trouble.