Yero, this is the English Only forum, please and thank you.
Hi QD. I haven't seen you in a long time - welcome back.
It makes more sense for Carol to be "singing" a "song" than "singing" a "tune". A "tune" is the musical sounds that make up a melody so unless she was simply vocalizing the sounds (do re me fa so la te do), it would make more sense for her to be singing a song.
It would make sense for "tune" to be used if you said that she was humming or whistling - a "song" means that words are being "sung".