Is this the film...

Where Cary Grant encounters a young girl (I'd say no older than 13 or 14) dressed as Mae West?

The girl lipsynchs to a record of West's "Frankie & Johnny" to a small crowd including a couple of sailors with a monkey. After she is done, Grant runs up takes her hand and comments "Goodness!" What diamonds!" The young girl responds, in typical Mae fashion, "Ahhh, goodness had nothing to do with it."