My husband and I have traveled to Europe a few times while we have had young children. Our first trip was to Hawaii when our youngest was only 3 months old. We took her along and don't regret it one bit. She was still so young, that she slept anywhere, anytime, and could eat anywhere, anytime too. We didn't bother with a stroller, we just carried her in a baby carrier on our chests. This worked very well! Though she wants to travel there again because she doesn't remember one bit of the trip.:)
Our next trip was in 2004, just before our oldest turned 4 years old. We decided to leave her home and prepared her for 'her' vacation with her 6 cousins as we prepared for our vacation to England, Wales and Scotland. I was gone for 3 weeks total. My husband came to join us as we were a week into our trip, so he was gone only a total of 2 weeks. He of course took her in the evenings after work and enjoyed the time he had with her before he left. Before I left, I put together things for her to enjoy on her vacation. We made a paper chain for her to count-down the days until Mommy got back and I pre-recorded some bedtime stories to listen to at night before bedtime while I was gone. We also called her every couple of days and were excited to hear about all the things that she was doing on her vacation. They did have quite a lot of fun without us! I do have to admit that I did miss her, but it was very nice to not have to worry about the time difference (about 7-8 hours) and about her schedule with naps and eating and all the traveling we did. There was also some things that I had to 'detox' her from when we did return. She had learned a few bad habits, but these few things were rectified pretty quickly. To this day she still talks about 'her vacation' and the souvenirs that we brought home for her. She made a few special requests and it was fun to surprise her with some treasures from Buckingham Palace.
Most recently we traveled to Sweden for three weeks, just this last summer. This time we took her, 6 years old by then, with us. It was very enjoyable to have her with us and for her to learn a bit about the Swedish culture. We kept emphasizing to her how lucky she was to be able to travel to Europe while still so young. Though she was exposed to quite a bit of 'European culture', we used these times and made them into good teaching moments. So while we did take her on the trip, we did leave her 22 month old sister home with family and friends. She enjoyed very much 'her little vacation' and got to go and see many fun things while we were gone. She spent a week at a different home, so she actually got 3 separate vacations. Also, with the time difference (9 hours) and ALL the walking and traveling we did, she just wouldn't have survived. I sent her with some of her favorite books and toys, and also a picture of us to look at when she was missing us. It often seemed that when we would call her to see how she was doing, that we missed her more than she missed us. When we got home we loved seeing all the pictures of her 'vacation' and she loved remembering all that she did. The only side effect that she had was a little clingy-ness, which is very understandable. She got through that though very quickly and has been none the worst.
So, I suggest that you will enjoy the trip so much more without your young child, and maybe when they are older, you will have an opportunity to travel together. This can be their time for a fun vacation of their own! Good luck!