The answer is C. Compound-complex.
A compound sentence is a sentence that contains two or more independent clauses connected by a comma, conjunction or semicolon. An independent clause contains a subject and verb and conforms a complete idea. A complex sentence is a sentence that makes a combination between one independent clause with at least one dependent clause.
In this case, the structure is the following:
Joan was singing because she was happy, and she danced as she sang. Both are independent clauses.
"because she was happy" is a dependent clause, specifically an adverb clause of reason.