I am planning our family's vacation for June next year, and we can't wait to go. Is this punctuated correctly? Am I correctly adding a comma before the conjunction "and" as this sentence has two complete sentences?

Yes, this phrase is well punctuated since the comma is before a coordinating conjunction that links two independent clauses.

An independent clause is a unit of grammatical organization that includes both a subject and a verb and can stand on its own as a sentence.