At the other day, when a student and I were working together, there was this need to introduce him to the expression: “It doesn’t matter”. Then, he showed me this song. It’s a cute, catchy song and I loved it! Listen to it! Have fun and work on it here!

Important! Song lyrics will ignore the rules of standard grammar and should never be used as a guide. The songwriter may pick a non-standard form so that it matches the rhythm of the song better, so that it rhymes better, because it is more evocative of a place or time, because it is in, or emulating a dialect, to be provocative or rebellious, and so on.

So “It doesn’t matter!” is correct.