Thank you Sandy, Billy and Q.
Just a few more points:
Sam Cowell was raised in America from the age of 2. (Although he was born in England). He returned to England at the age of 18, but his early influences were in the American South.   
It will be George Coppin who was responsible for the Australian references, I believe. He said he wrote "We're All Dodging" but they all claimed to have written the songs they sang. I really think he did at least re-write it.
Charles Dickens was a good friend of John Lawrence Toole. They walked the streets of London together looking for "characters". Dickens also frequented the musichalls where Sam Cowell and others performed.
It is indeed a tangled story, but the performers playing "The Dodger" do seem to have taken him from London to Ireland, America and Australia. I'll be delighted if someone comes up with an earlier "Dodger" in America.
I enjoy puzzles like this one.
I'll post the words to "We're All Cheating" Cheers Joy