Thank you for your question. If your premise was that only reported actions of the Prophet (saw) are allowed, no matter what society or context, and that everything else is forbidden, then travelling by plane would not be allowed as planes were not invented at the time of the Prophet (saw) and since he (saw) didn't travel on one, travelling on one is not allowed.
However, if your premise in following the sunnah is that all actions are allowed, except for those forbidden by the Prophet (saw), and that the rest of his (saw) actions either preferable or obligatory (that distinction being decipherable through certain means), then that would not necessitate travelling on a plane being impermissible.
Most scholars and believers work on the second type of premise and others like it rather than the first, and that is why travelling by plane (anywhere) is allowed by the vast majority.
May you always be successful.