My daughter is taking a friend with her on our cruise (2 weeks and counting!).  Our travel agent gave us a form to have notarized by the child's parent stating we have permssion to take her out of country. Also, one parent is deceased so she is sending the dc.  Has anyone done this before? Is there anything else we need? My fear is getting to the check-in counter and not having what we need to board the boat.

you might want to get a form giving you the medical power of attorney.  Always better to be safe and have to much paper work with you.

My wife and I have cruised with our daughter bringing a friend along ( pre-teen) and also another trip with our 6 year old grand-daughter without any problems. Along with the notarized permission slip you will need proof of citizenship. ( We were only checked on returning to US ) 

Will the passport prove citizenship?

yes, and it is the best proof of citizenship

Thanks!