I would, meet them first, make sure that the child seems to operate within rules that you are happy with (ie the mum is not a "let her do anything" type if you are not like that too) and make sure the child is happy with the idea. Also I would ask for the dads number as an emergency contact for the weekend incase something happens or she is upset etc. I would also make it clear this is a one off!
But then I am a hopeless romantic at heart and would do anything to see my single parent friend matched up and happy