Yes, apply a clear coat over stain on a fiberglass door is a must. Stain alone won't last very long. This also applies to factory stained and finished fiberglass doors that are just starting to fade.
There are several good finishes that could be used. My favorites are McCloskey Man-o-War marine spar varnish and Varathane Spar Urethane. Both have great adhesion and weather resistance.
If your door is already painted, solid colored paint, then no additional protection from a clear coat is needed.