Hi Lele...
First, let me say good luck at the Doctors. I hope all goes well!!
Whenever I take Zoe to the vet, I take him a a critter keeper. It's a larger one, about 12"L x 6"W x 8"H. I line it with a tea towel (dish towel? The kind you dry dishes with, that isn't made out of terry cloth...don't want any caught claws)I usually put it into the microwave to warm it up a bit before I put it in the container...I'm sure I don't need to tell you this but: make sure it isn't too hot. 
Then next, in goes Zoe. Then another tea towel over top of him. Also lightly warmed.
Getting him there is always the easy part...it's getting him home that poses more of a problem. By the time I leave the tea towels have cooled...Zoe is stressed from all the handling and so on.
I like to keep the towel right over his head, like a little tent. I don't want all the scenery flashing by as we travel to and from the car etc. to stress him out even more than he already is.
Again, I hope everything goes well for you and Luna. Keep us posted, I'm anxious to hear what advice the Vet gives you!
Thanks,
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Kim