Not to be contradictory with anyone, but we have traveled extensively internationally with our kids (now ages 16 and 13) since the oldest was 4 months old (we went to Italy then), and have really enjoyed all of it.
There is definitely some variation with respect to temperament, though, and I know we were super lucky in that regard. Even so, the plane flights can be tiring, especially since we prioritized not disturbing others over our own comfort - I nursed a ton in the air, and DH and I hung out in the galleys, and brought along carry-ons with every possible contingency - and we were able to keep both babies from crying in flight (at the smallest sign of a hiccup-y gasp of air we would spring into action). We tended to divide and conquer, so that one of us would be exhausted when we arrived, but the other one would be rested, and able to take care of the first day, on the ground logistics. If you are willing to put up with that, and can spring back from jetlag-like effects quickly, you will be fine.
Most of our trips when the children were young were independent (fly somewhere and get a flat, or rent a car or take the train), but we did do three big cruises starting when our younger one was just shy of one year old - Greece, Egypt, and Turkey for the first one, Northern Europe (Baltics + Russia etc.) a year later, and then around the coast of South America a year and a half after that. It is absolutely amazing not needing to pack and unpack again and again, and I would do those trips again in a heartbeat. At the same time, we haven't traveled like that since then, because we found that cruises didn't really perfectly fit with our family's style. Everyone is different in that regard, of course!