It may be possible that the breeder didn't know the breed of the dam, and just refered to her as a galloway. Galloway is NOT a breed. It is a term for the hieght range 14h-15h and is used in hacking, as well as pony and hack. I.e. Pony Hunter, Galloway hunter, etc. All different height classes.
A Waler is a horse that is descended from the horses used by the Australian cavalry. Similar to the Australian Stock Horse, both breeds share some ancestors and attributes. A waler/ARP cross would be quite unusual.
If he is an ARP cross, he would be fairly small, yes? If he is indeed a galloway he will be between 14h and 15h. Any horse can jump, but unless he is outstanding he will probably be limited to smaller fences because of his height. But there are always exceptions.