--any celiac tests--anti-transglutaminase or anti-gliadin--that measure the levels of immunoglobulin A for antibodies to gluten will not be accurate, as she apparently has low levels of immunoglobulin A overall (an issue that in itself warrants some investigation; there are people with congenitally low levels of certain immunoglobulin classes, and they sometimes have a bit more trouble fighting pathogens than others).

But bottom line, blood tests for celiac will probably not be accurate for her, and she may need endoscopy with villious biopsy to confirm or rule it out.