Anna, I agree with the earlier posts.
You have a young couple growing in the north east, farming stock. Stonehaven isn't that far from Aberdeen at all, and you say that although George was born in Stonehaven they later lived in Old Machar, and then moved on to Peterhead, so I don't quite understand your original question about 'why move all that way north?', because all these places are in the same part of the country.
Looking at SP, I found some births that could be your George, though it may be you have already ruled them out? George Greig born in 1806 in Fordoun, which is not far from Stonehaven. When giving information for the 1841/51 census it wouldn't be unreasonable to assume that someone gives their general area of birth, rather than the exact village, and if born in Fordoun summing it up as 'Stonehaven' would be fair enough.
His parents were George Greig and Ann Smart, not sure if that rings any bells? There were 3 others George Greig births in 1812, 1816 and 1818 but their fathers are listed as Thomas, James and William, so if you already know your George's father was also George we can rule them out.
As to why they moved from Old Machar, which is a rural area a bit north of Aberdeen, no idea but it's possible that they ween't making the living they needed to in that area? From Old Machar the road heads up through Elllon and Hatton to Peterhead and if there was work up there servicing the fishing fleets they may have considered it a better prospect. The fact that they headed to Australia a few years later may mean that they were struggling to make ends meet, as so many were, and just kept chasing the chance of a better life - hope they found it.
