Too funny. I'm 60 and I remember this song and every once in awhile over the years I'd sing a couple of lines to my daughters, and then now to my grandkids. However, of course I was singing the wrong words. I had this song on a 45 record too like some of the others commenting here.
I was singing:
Do do do do do you know what's happening at the zoo?
What's happening at the zoo? I swear that it is true!
Do do do do do you know what's happening at the zoo?
(then I was kind of blah, blah, blah as I couldn't even make up words haha)
THEN I'd sing
"The giraffe is laughing. YUCK YUCK YUCK (high pitched),
Can't you hear him laughing? YUCK YUCK YUCK
It's not at me that he is laughing YUCK YUCK YUCK
So he must be laughing at YOU!

Obviously now I know those are NOT the right words (although they do make sense haha)

Found this online tho https://www.youtube.com/watch?v=_FrlUECrf_c

Hope that link helps as I believe it's the original singer of it.

Kathryn Mattatall, Nova Scotia, Canada

PS - My mom used to sing The Wedding of Jack and Jill song to us when we were little, and I had NEVER met anybody who knew it, and I couldn't find it online until last year.....when I discovered that not only did somebody outside our family know the song (probably from the 1930's when my mom was little) but that there were other verses I didn't even know about! I'm sending the link to that one for you too....great song and I always sang it to my kids and grandkids even now. I even sang it to school kids years ago when my daughters were in elementary school, and had those old Red Rose Tea nursery rhyme figurines and told them the nursery rhymes of the characters in the song before singing it so it would have meaning to them. haha   I guess Laverne and Shirley also did a bit of this song...nice to know I'm not crazy and the song does exist! https://www.youtube.com/watch?v=UNpmsvjPLr0