"Christmas Wrapping," dear JennieG,
is a North American single, which would explain
an Australian not hearing it.

It's been around for a couple of decades only,
but it is wry and witty
and literate enough for progressed adolescents like me.

It's also kind of hard to understand the words sometimes!
The lead vocal is intended to sound like a disaffected single woman,
in fact the first words are Bah! Humbug! However:

the story has a happy upbeat ending
it's nondenominational, nothing religious
the music is a pop / beat blast,
especially those instrumental breaks with the trumpets.

I smile every time I hear it.

Now, let's see if I can link to the recording
WITH the lyrics printed out.

Christmas Wrapping

As for the album cover photograph,
the lead vocalist is in the lower right-hand corner.
Her name was Patty Donahue (deceased).