Shirley Temple doesn't refer to the singer of the song, but to slang for the act of dressing up like a younger girl.
David Calder (Father Michael Harvey) would later go on to star again with Robbie Coltrane in the Bond film "The World Is Not Enough" (1999).
Shirley Temple is unlikely to have recorded How Much Is That Doggie In The Window. The original version by Patti Page was released in 1952 when Ms. Temple would have been 24.
Ms. Temple is best known for the song On The Good Ship Lollipop. It is suspected that Granada didn't have the rights to include that song in the programme.
In 50 minutes we see a prostitute singing along to How Much Is That Doggie In The Window. The record us a modern pressing in the Arista label.