This rhyme goes back at least to the 1840's…

Two Little Dogs - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image

Notes

*A fender was a metal frame or screen placed in front of an open fire to keep the coals or sparks from going out into the room.

Here's the version from The Big Book of Nursery Rhymes (circa 1920), edited by Walter Jerrold (1865 – 1929) and illustrated by Charles Robinson:

Two little dogs
Sat by the fire,
Over a fender of coal-dust;
Said one little dog
To the other little dog,
"If Pompey won't talk, why, I must."

Thanks and Acknowledgements

This rhyme can be found it in The Little Mother Goose (1912), illustrated by Jessie Willcox Smith, and printed in the USA. Illustration from The Big Book of Nursery Rhymes (circa 1920) edited by Walter Jerrold (1865 – 1929) and illustrated by Charles Robinson (with a little graphical editing by Lisa Yannucci).