As a former teacher (in both MO and IL) I agree that you don't want to send her if she feels terrible b/c she will do terrible on the test. BUT (and this is a big but)...I must admit that I think if she's well enough to go and do the tests with the class she absolutely should, even if you send her for testing and pick her up after it's over. I know that probably sounds crazy b/c it's just a test, etc. etc., and yes that's true, but this is a big deal in every school. She can make up the tests, but when she has to make them up she'll have to miss more class time and be in a room with a bunch of other kids doing make up tests. Rarely do the make-up test kids take as much time or give it as much effort as they would the first time around, mostly because they're secluded from their peers and they want to get back to class, not because they're lazy or anything like that, because I'm sure she isn't that!!
In th end, her health absolutely comes first, but my best advice would be talk to her teacher and see what her teacher really thinks. I hate, even in my written response, to put so much pressure on tests like these, but the fact of the matter remains that the school boards and governments do, so as teachers and parents we have to do the same, otherwise we lose funding, not to mention we lose good teachers and good schools. In the end, if she does stay home, I would at least ask the teacher for any materials they are studying or reviewing to help her be more successful on the tests so that she'll be more prepared for make-ups. I hope this helps! Good luck and I hope she feels better soon (and not so she can do the test! ;)