Hi Bob,
Shipping records for that time period are very patchy and mostly only survive for the port of Hobart so your chances are not good.
George's obit says "....The deceased was a jockey, and rode in many races in England before coming to Victoria...."
If the indication is that he arrived as a young man and he was an accomplished jockey/groom then he may have arrived as an escort for imported horses.
In 1844 a George NEW was the jockey on a horse called Whalebone which won the Merchant's Purse.
http://trove.nla.gov.au/ndp/del/article/66017124Halfway down the first column.
The horse was owned by Captain Edmund Isham of the 51st Regiment who was in Tasmania at the time (arrived 1838 on the Marion Watson). A short obit here
http://www.mocavo.com/Hardwickes-Annual-Biography-by-E-Walfo...Something interesting to note is that in 1845 Whalebone was owned by a Mr STEPHENSON. The jockey was named GARRUTY and there are other mentions of a jockey named as J. GARRETY. A John GARRETY was one of the witnesses at George's wedding in 1844.
http://trove.nla.gov.au/ndp/del/article/2948977In 1884 there was a series of articles (12 altogether I think) published in the Launceston Examiner titled "Some Old Tasmanian Racing" where there is lots of information about racing and the people involved in the 1830s/40s. I can't see a mention of George but it would be worthwhile reading through the articles to see if anything has been missed in the OCR translation. It gives you a good idea of what was going on at the time and he does lament a couple of times that the jockey's names were rarely mentioned. He does also mention a couple of jockeys who came over from England with particular thoroughbreds.
Do you have any birth certs for George's later children who were born after civil reg started in Victoria? His place of birth on those would be more reliable than a death cert.