I was too chicken to do my son's at 2, but I knew at his 3-year I better get it done, plus the dr had ordered a routine CBC as well (which indicated that his iron was low, which involved 2 more lab trips--yay, but I digress). What they had me do at the lab, and it helped that they were young girls who just love kids anyway and feel horrible when one has to have blood drawn, was to hold my son on my lap, my legs over his so he couldn't kick, my arms around him holding the upper parts of his arms, and he had his favorite Curious George doll with him. He did cry, but it went quickly and they offered him stickers afterward. They didn't have George stickers the first time, but they had some the 2nd and 3rd times so my son was happy about that, and by the time we got back to the car, he was smiling and jumping for joy again. He just wanted the bandage off ASAP.
Your daughter will be ok, and she'll probably forget it even sooner than my son did because she's younger. Above all, try to be strong about it yourself, be reassuring but act like it's not a big deal. If she sees you're upset, it'll be worse. GOOD LUCK!
Oh and I took him to lunch or did something fun afterward--kind of like "making it up to him". Makes them forget even sooner...