No! We are not connected but there is some coincidence in name. My great,granduncle was also James Petrie. He was born at Kennethmont, Aberdeenshire, in 1823, the year after your ancestor. He came to Australia in 1854. He was probably an assisted migrant and the ship berthed in Sydney.
On the Immigration lists his occupation was that of farm labourer and he said that he had a brother living in Melbourne at the time of his arrival (my great grandfather married to Catherine Jane Turner with one three year old daughter). He presumably followed his brother to Melbourne and then to Sandhurst (Bendigo) where he was a goldminer in the Gold Rush in Victoria. He is listed as one of the electors in the first election held in the State of Victoria. His franchise was the result of his holding a miner's right. Later, I believe he assisted in the running of a general store with his sister-in-law. James died at the relatively young age of 37 in 1861. He is buried in Back Creek cemetery in Bendigo. This is probably of no help, but I thought I would share it with you. Someone out there may also find it helpful.