Lady Gaga -- Goo Goo GaGa ... Soothes Crying Baby

Lady Gaga is flat out baby crazy ... which is no surprise given her last name is gaga.

We see babies get handed to politicians and celebs all the time ... but when you turn one over to Gaga, you'd better be ready for a show.

And Gaga -- who was in Australia prior to her artRAVE Tour -- did NOT disappoint.

There are no small gigs for Gaga ... especially in front of a live audience ... so this lucky kid got itself a PITCH-PERFECT performance ... which we're guessing was done for the benefit of the cameras.