D..
Make sure you call them up in advance and ask them if they have butterfly needles. I would NOT use their services if they don't use them. If they don't have them, ask the doctor to find you a place that DOES, and then make sure the lab is covered by your insurance. You have time to do this and it's important that you make sure you've covered by the insurance wherever you end up going.
The butterfly needles are so much easier on children, really and truly. It will help prevent crying jags and fear everytime she goes to the doctor. You also want to hydrate her very well so that they can get a successful "stick" the first time. Lots of liquids the night before - don't worry about her wetting the bed. Lots of liquids in the morning before going in for the blood test.
Make sure you are in there with her and tell her to look at you. When I have blood drawn, I actually tap my leg with my other hand, hard. That takes some of my attention away from where the needle is sticking. Maybe you can have your daughter do that, if she is able to without jerking her arm. I always told my kids that relaxing is the magic trick for anything involving needles. I would hold them and say "relax, relax, relax" gently. They actually asked me to hold them until they were very big, LOL! For bloodwork, I was right there with them too, talking them through it and trying to get them to pay attention to me instead of their arm.
I didn't give anything after it was over, but others might have some ideas about that.
Good luck!