Is peninsula a proper noun

Well, it depends on how you're using it:

If you say, "That peninsula in Pennsylvania is large," then no, it is not.

But if you say something like, "The Pennsylvanian Peninsula is large," then yes, it is.

If it is part of a name, then consider it proper. Kind of like ocean, because you would capitalize the ocean in "Pacific Ocean" but you wouldn't capitalize the ocean in "The ocean off of the Pacific," you know?