A child of a single mother is specially anxious about being abandoned. That's natural. So it is natural that she wouldn't want to sleep away from you. Actully, one of my children wouldn't sleep away from me either and he is much older already. It is fine in terms of her.

So, it is your need for a break that is the issue. I think life with your daughter will be much easier if you let her be and respect her preferences. Then you won't feel a need for a break because you will have a good time with her. You can get a relative or a friend to come by for a visit and take some of the load off, but overall, she is too young to have to care for your needs and give up on hers for your sake. She shouldn't sleep away from you because she is obviously not ready.

Read a good parenting book about the value of respecting and trusting the needs of Children. Raising Our Chidlren, Raising Ourselves, is my favorite. But there are others like, Kids are Worth it, Unconditional Parenting, Your Competent Child etc. Learn learn learn. We are not born knowing to parent. Dont' blame yourself, yet do learn and apply kind parenting.