While you can have a suppressor on your gun while traveling, it is generally not recommended. There are a few reasons for this. First, if you are stopped by law enforcement they may not know that you have a legal suppressor and could perceive it as a threat. Secondly, suppressors can be difficult to transport because they are large and bulky. Finally, most airlines do not allow firearms with suppressors in their baggage so you would need to contact the airline ahead of time to make arrangements.
While there are some drawbacks to having a suppressor on your gun while traveling, there are also some benefits. Suppressors can help reduce noise pollution, which can be beneficial if you are shooting in an urban area or near sensitive areas like hospitals or schools. They can also help reduce recoil, which can make shooting more comfortable and accurate.