I picked this up from another chord site, so maybe give it a go? Looks the same as GUEST's above, but with the bridge added.

I remember this song as a child. I was questioning why someone was out so late with a baby in a pram.....

[G]Gee but it's [Em7]great after [Bm7]bein' out [Em7]late
[G] Walkin' my baby back [E7]home
[A7]Arm in arm [D7]over meadow and farm
Walkin' my baby back home[G]

We walk along harmonizing a song
Or I'm reciting a poem
One kiss then we continue again
Walkin' my baby back home

We [Bm7]stop for a while, she [F#7]gives me a smile
She [G]snuggles her head to my [Bm7]chest
We [D7]start in to pet and [A7]that's when I get
[D7]Her talcum all over my vest

Then after I kinda straighten my tie
She has to borrow my comb
One kiss then we continue again
Walkin' my baby back home