Sounds like it is related to related to My Bonnie Wee Hen.

And also this, found on a web site of Some Old Scottish Street Poetry:

Once ah had a wee broon hen
It had a wee broon tail
Ah sent it fur an ounce o' snuff
It never came back again
Noo it's deed and in its grave
Mony a year ago
God bless ma wee hen
It never came back again

Ah had a funeral
Fur ma wee hen
Ah had a funeral
Fur ladies and gentlemen
Ladies and gentlemen
Count to ten
God bless ma wee hen
It never came back again.