Slang but certainly not rhyming - it's American:
"You can credit America's youth and their love of counter-culture slang for the connection between the two seemingly unrelated words � "dogs" and "feet." According to Tom Dalzell, author of Flappers 2 Rappers: American Youth Slang (Merriam Webster, October 1996), it was during the Jazz Age of the 1920's that "dogs" was used as a noun to indicate feet. For example, "my dogs are barking" in 1920 speak translates to "my feet are hurting" in modern speak."