I always picked mine up in either their small crate (full of towels so it is comfortable and mine opens from the top) or my over the sling carrier. The little ones are really out of it at that time so it is whatever you are comfortable that you can lift them out very gently. Then once home I would put them in their bed with a blanket over them so they do not catch a chill if they are still sleeping. A number of times mine would wake up and want some water and just a little food as they have not have either for a very long time (go light on food/water). They might want to go the bathroom but for the most part after a little water/food they go right back to their bed and go back to sleep. Really your little one should do fine and the next morning they are usually back to being a terror
P.S. It is safer for your little baby not to have its paws on the ground at a vets office as to many diseases can be picked up from the sick dogs coming in. My vet always told me to never put one of my Yorkies on the ground and make sure the exam table has been cleaned off from the previous dog/cat.