Pitch your yeast BEFORE you transport.
It's safer to do it at that point, then any other part of the fermentation process. You'll get plenty of aeration, your yeast won't be harmed, it will get thoroughly mixed with the wort, the yeast has the best chance of taking hold before anything bad gets in, AND when fermentation happens it would clean up anything that might have happened during transit.
If you wait too long you end up like this guy who
didn't take my advice.
One of the issues folks don't realize is that a carboy or bucket is not an airtight enviroment. It's really not supposed to be, and an airlock, though very important is still only a delicate barrier between the beer/co2 cushion and the outside world. Sloshing the beer even with an airlock on opens up the beer to both oxygen and to the possibilities of nasties getting in (the airlock could even get dislogded) it's not the best way to do things, but adding the yeast ahead for the reasons mentioned, kinda hedges the bet.
And that's why I caution folks not to move it with an airlock once beer is in there....you have a greater risk of oxygen/oxygen getting in there during all that whipping up in transit.
But you don't want to wait too long.