My DD did this at the same age too. She went with some friends from sixth form after A Levels had finished, and before they were due to go to uni. They loved it and had an absolute blast! 😃
Make sure that she has good travel and medical insurance. Take it out for her if necessary. Then just see her off cheerfully at the airport and wish them all a great trip.
It's natural to be anxious, but you know you have to keep it under wraps.
Remember that this is Europe, a relatively short trip really and all only a fairly easy and quick flight away if she should need you (unlikely).
I do understand your feelings. This time last year my youngest (DD3, then 20, now almost 21) was heading off to Paraguay to start the first leg of her obligatory year abroad. I was anxious and tearful leaving her at the airport, and so was she. Not that I didn't think she would manage, but it was just so far away if anything were to go wrong (it didn't, even though there were occasional wobbles), and fear of the unknown. She made friends with people going on the same scheme and they were all fine. Her older sister travelled out for the last couple of weeks and they had a great time hopping around South America and doing the Inca Trail together. She also knew that if she really needed me then I would have made a way to get out to her.
She's now coming to the end of the second leg of the year abroad which she has spent in Italy. We have visited her there, and are going out again soon for her last few days there and she will be coming back on the same flight as us.
Try to relax. Your DD is starting to spread her wings now, and she'll be fine. You have to step back and let her go, hard though it is. Just ensure that she knows you are there if needed.