A6 is one-quarter the size of A4, which is more or less the size of 4"x5" photo. I would say that any printer able to print photos should be able to handle this size. But I think (and I might be wrong) that only ink-jet printers can do that.
When choosing an ink-jet printer: Look for a model with separate color cartridges. This way, you don't have to replace the whole color cartridge if only blue ink ran out, and in many cases you might be able to find lower-priced after-market (non-original) ink cartridges.