My dog is licking and pawing a blanket, almost like she is suckling?

Since you don't know about her puppy history it could be possible she was taken away from her mother too young. Our dog that we got was 6 weeks when she was taken away and she has a nibbling problem like she is constantly trying to suckle - and she is 2. As long as it is not hurting anything, I would just let her do it.