B.F.
I'm so sorry to read that you are having to go through this. It's heartbreaking to be sure!
I have had to live through some strange (although minor, it was a big deal to them) procedures with my sons, and it does just break your heart.
One thing I've learned is that it's important to them that I stay calm and matter of fact. I also tell them ahead of time what to expect in as simple of words as possible to remove the fear of the unknown. If it's going to hurt, IMO it's ok to tell them "it might hurt a bit, but just for a minute and then it will go away. If you squirm around it's going to be worse. I'll be right there with you the whole time and it will be over before you nkow it and we'll go [insert reward treat here]."
Now, I know she's really young, but she'll read a lot from your demeanor. It's important that all the caring adults are calm and matter-of-fact. You can freak out later, but not while you are with her. You HAVE to do this.
I'd let her know that it's ok to be scared, that even a lot of grownups get scared sometimes, but it's really important to keep her body safe. Keep reassuring her that you'll be right there with her, that everyone (drs and nurses too) care about her and want her to be safe. You don't want her to think that the medical staff is the enemy.
I don't know if there is any way you can be holding her or laying down next to her for the procedure, it might be worth asking. I have found that physically holding down a child makes them panic big time, and you should try to be creative in finding a way to get around physical restraint.
I know this is really hard for all of you. After it's all done, I'd make sure to spend some time reading books about going to the dr, and role-playing dr with her so she can work through her fears. (You might do that ahead of time too).
Any way they can knock her out for the procedure??