A complex sentence has one independent clause and one or more dependent clauses.
A compound-complex sentence has more than one independent clauses and one or more dependent clauses.
Your sentence has three clauses, 2 independent and one dependent, so it is compound-complex. I will mark the clauses in color. Incidentally, the first independent clause has two verbs joined by a conjunction, but it is one clause.
Alice guessed that he was looking for his fan and white kid gloves and good-naturedly joined in the hunt, but the Rabbit's belongings were nowhere to be seen.
orange = dependent clause