Does anyone know of a 1.6 or 2x teleextender that will fit on the Canon XA H1? I'm considering getting one for nature photography where the extra focal length can occasionally be useful? If one does exist, any comments about the amount of image degradation it will introduce?

Well, considering the lens on the XH A1 is fixed, this could be a tad difficult, since usually extenders go between the lens and the body. Or are you talking about something to attach to the end of the lens? I've not seen anything like that for the XH A1.

If you mean the former, you may have more luck in the XL H1 forum, since this model does permit changing lenses.

Try looking at Century Optics' stuff for the Z1--it too has a 72mm thread and might fit.
Of course it will soften up the image some. By how much, and whether the result is acceptable can only be determined by some hands-on testing.