Three words,
. . . ben
. . . a
. . . dryl
Be careful with this suggestion. Ethics aside, you should never give a new medication without consulting a doctor first (especially in this case, because there aren't instructions for infants on the bottle) and it's a bad idea to give any medication for the first time on a plane. (the kid could have an allergic reaction to an ingredient, then you're in even worse shape)
Also, from experience my kid wakes up as soon as the dose wears off and in an even crankier mood than he was before. For this reason, I hate giving him benadryl in general (though at times he does need it for a reaction) and I rue the day that he'll need it on a plane flight that's longer than 4 hours again.
Also, it's a pain in the butt to get through security, because it only comes in bottles larger than 3 oz.
In general, I've found that traveling with infants on planes isn't much different than taking care of them anywhere else. It's once they start walking that travel becomes difficult. Bring about twice as much perishable stuff as you anticipate needing for your whole travel time (not just the flight time - include travel time from home and until you get to somewhere you can replenish your supply at your destination). One suggestion I've heard is to pack 1 diaper for every hour of travel, and I've never gotten done with traveling with my kid and thought "man, I wish I would have packed fewer diapers." Same thing with food.
The extra change of clothes/shirt for yourself suggestion is also very good. I spilled a bottle of water on myself and my child on a plane once. That extra shirt was very well loved that day.
Bring some kind of carrier on the plane with you. You can't use it during take off or landing, but you can use it to walk the baby up and down the aisle hands-free.
Another good suggestion I've seen for formula users is to pre-measure out most feedings.
