I have the song sheet in front of me and it's called "Everybody loves my baby". It was learnt by my friend when she was a student in Holland and there's no other identification on it. The teacher could have found it anywhere!
I tried to Google it and came up with Doris Day but that's not it.
The closest one looks like the Boswell Sisters (and if there were four of them, that would fit very well).
The words need four singers and when we do it, first one starts and then the second comes in, then third, then fourth until everybody's going!!!
The words I remembered aren't quite right - here's the way we do it from our song sheet:

First singer (deep voice):

Baby cares for,
My baby cares for,
My baby cares for,
My baby cares for only me.

Second singer (higher voice):

Baby just, baby just, baby just cares for,
Baby just, baby just, baby just cares for,
Baby just, baby just, baby just cares for,
Me-e ooh-ah

Third singer (also high voice):

My babe I sigh for,
My pretty baby I die for,
'Cause my babe don't love nobody but me,
I"m so lucky.

Fourth singer (soloist?)

Everybody loves my baby,
Baby cares for only me.


At the bottom of the page there's another little bit of music that says "Begeleiding" and has
Baby just, baby just, baby just cares for, 4x

When it's all going it sounds a bit like the Andrews sisters jazzy 1930s music.

Robyn