First, some disclaimers. I don't know Judeo-Arabic, and I don't know Arabic that isn't Judeo, and my knowledge of Hebrew is very minimal.
Now on to the story. You may have heard that the god of the Jews is not the same as the god of the Muslims. Our god is God, and their god is Allah. You may also have heard someone reply that "Allah" is simply Arabic for "God" and is used by Arabic-speaking Jews and Christians.
Mr. Mississippi F. MacDowell's always excellent blog On the Main Line (at least it's always excellent when it isn't over my head) recently published a 9th- or 10th-c. passage in Judeo-Arabic with English translation. It's in Hebrew script. Take a look at the second word from the right in the second line. It appears to be "Allah," and it appears to mean "God." This "appears to" stuff isn't meant to be snide--I actually don't know, so I don't want to make a more definitive statement. But I'm reasonably confident about it.
As always, comments are invited, and comments from those of you who actually have a clue on this are especially welcome.