I've been thru it w/my son....twice! I was dreading it, thinking that he was just going to go balistic. Bottom line was that he cried way more for a haircut than he did getting blood taken from his arm! The first time he had it done, he didn't even make a peep (he was 1 at the time). The second time (when he was 2), he wimpered a little bit, but that was it.
The nurse or whoever draws the blood will most likely have your daughter sit on your lap, and they will also want you to help hold her arm still. In all honesty, this will probably be much harder on you than it will be on her.
Good luck! And you are indeed doing the right thing. Lead poisoning is nothing to fool around with.
D.