You need to bear in mind that places of birth for people do change, depending on where they are living or indeed depending on what they want to admit to. If he was living in, say, the village of Belstead, he would say in censuses and official documents that he was living there. However, if he moved elsewhere it was often easier to name the nearest large town ie Ipswich as place of birth. Ancestors are notorious for changing their birth places, dates of birth and suchlike, often because places and dates had less importance to them in those days. A lot of people would just take a rough guess at how old they were. And if he was in Australia I'm certain he wouldn't have bothered to name a tiny Suffolk village as his place of birth but would go for the nearest large town ie Ipswich. So I don't think you should confine your search for this particular James Garnham solely to Ipswich; and neither should you take the date of birth as fixed, but rather as a rough guide.
Best of luck with your search. If you manage to link him to Gosbeck, Tattingstone or Belstead let me know as I have plenty of info on the Garnham line in those villages, none of which is particularly far from Ipswich.
