It's not going to hurt anything to call your doctor and just ask. You will probably talk to the nurse, who will ask you a bunch of questions to get a better idea of how your daughter is doing, and then the doctor will decide whether or not a visit is warranted.
I have zero medical training, so please keep that in mind. I can't remember my pediatrician ever wanting me to bring the kids in for any temp less than 102 (maybe even 102.6), and she's never ordered blood work. She did order a urinalysis once, but that was when we thought our youngest might have a urinary track infection.
I find it very strange that your doctor would order tests for such a low temp, but I didn't go to med school, and she did!
Give her a call. Let her know what's going on and let her tell you what is the best thing to do. Try not to worry about a blood test if that's what the doctor decides is best. It's true that your daughter won't like it and will be in pain for a moment, but it really is just a moment. She won't remember it 5 minutes later. Still, I doubt your doctor will order that test.
Don't be afraid to call your doctor, ever. That is what she is there for, and I'm pretty sure she's been called for less important reasons than an elevated temperature.