BrE native, not a teacher
"I danced for a whole hour" is correct. This is the most natural sounding formulation.
"I danced for one whole hour" would also be correct, but
"I danced for a whole one hour" is wrong. You can't have the indefinite article (a) and 'one' for the same noun (hour).
The question should be "which is correct?", or "which is right", not "which is proper".
hope that helps