There are hundreds of Gills living in Wimborne Minster from at least the middle of the 17th century up to the 19th century. Many of them left wills - for instance, a James Gill, butcher in 1786; and a John Gill, wheelwright in 1762. The latter mentions his sons John, James, Thomas and William; and his grandsons James and Thomas. The two sons may be the John (wheelwright) and James (surgeon and apothecary) mentioned on an oath connected with John's wife's (Margaret) death. There are also four PCC wills (including a James, John and Betty who all died 1796-1800) which can be read online for a fee of £3.
There is a strong possibility that they will be connected, but I would caution against working down from these. As you say, there is a James Gill baptised in 1799, but his ony sibling mentioned in the registers is John baptised in 1803; there is no sign of a Charles or George.
Do you know the occupation of your James Gill? If he was a carpenter/wheelwright that would be good!
These are presumably connected to you:
http://archiver.rootsweb.ancestry.com/th/read/DORSET/2000-01/0948025973http://boards.ancestry.co.uk/localities.northam.canada.newfoundland.notredamebay/505/mb.ashxThere is a tree on ancestry which suggests that James was born in 1799, but Charles in 1831, which seems a big gap. Do you have any more information on Charles and/or George?
Banns of marriage were called between a James Gill and Jane Cole in October 1820 in Wimborne, and then, in Jan 1821, James Gill is being sought in connection with the bastard child of Jane Cole. Jane died in 1833 aged 34, so was the same age as your James Gill. Perhaps he was running away from something! It might be worth asking the Dorset History Centre to look at the document (PE/WM/OV/10/5/33).
Richard