Many versions of "Darling Little Joe" or "Little Joe." Randolph has four, and one from Max Hunter is in the DT as "Darlin' Little Joe."
This one from Randolph, with music-

Lyr. Add: Darling Little Joe (2)

Oh mother, dear mother, you may miss me for awhile,
For in Heaven no larger will I grow,
And any kind angel will know at the gate
When you call for your darling little Joe.

What will my kitten do, mother, all alone,
Will she stop in her frolics for a day?
Will she lie on the rug by the side of the bed
As she did when I went away?

Then love Tige, mother, my poor little dog,
For you know he will mourn me for true.
Speak kindly to him and often of Joe
And pat him on his brown shaggy head.

What will old Thomas the gardener say
When you ask him for flowers for me?
Will he give you the rose he has tended so long,
The first fairest rose on the tree?

I saw the tears coming in his honest old eyes,
And he said 'twas the wind brought them there,
As he gazed on my face growing paler each day,
And his hand trembled over my hair.

There's poor Uncle Jack in the far-away camp,
He'll feel sad o'er the letter that you'll write.
Only tell him, dear mother, I have gone to the front,
Marching nearer and nearer the fight.

Mrs L. A. Thomas, Anderson, MO, 1927. Randolph, vol. 4, No. 712A, pp. 176.
Other versions in Randolph have the 1st verse about the birds.
This song seems to have been a composed piece that caught the fancy of many folk singers. Similar tear-jerkers in threads and the Levy and Hunter Collection about orphans dying, etc.