Robbie, a quick web search shows lots of answers. I quite like this one...
The phrase “as happy as Larry” originated from a character’s name, Larry. It was first used in a printed version by G. L. Meredith, a Kiwi in 1875. The first person here is plural and the phrase is used in its original form, “We would be as happy as Larry.” Another use has been found in Barrier Truth, a book written by a popular Australian, Tom Collins in 1903, “I was as happy as Larry.” While the name Larry has been a famous simile, there are two possible inspirations for the name and the phrase. Firstly, the word might have been derived from “larrikin”, a slang used in Australia for a person who is either careless or causes trouble. The second option might have been derived from the name of Larry Foley (1847-1917), an Australian boxer, who had never lost a fight.