Our son was always a great traveler so we never had issues on planes as he was so excited to be on one that he wanted to see everything.
A few recommendations that I would make with this being his first flight is:
1. Do NOT do the preboard. You could be on the plane a significant amount of time longer waiting for anything to happen and it can get boring for a child.
2. Get him lots of exercise and let him run around the airport BEFORE getting on the plane.
3. IF it's not a full flight ask to be moved to an area of the plane where there are not as many passengers so you can spread out a bit. That way if he wants to move around a bit it won't be a big deal.
4. Normally they will give your son some wings or if there is time they will let them come up to the cockpit and take a look. The last time we flew we got an upgrade to first class and they took our son into the cockpit and let him look around. He came back talking about all the different color buttons and what they were for..... (Doesnt always happen but sometimes).
5. Make sure you bring a couple videos and the DVD. Bring something to eat that he will eat at takeoff and landing. That's the two worst times for ears popping (due to pressure changes) and swallowing will relieve that pressure. Our son is old enough now where he can do fake yawns to pop his ears but at 13 months that is not going to be possible. You can pack some crystal light sugar free drink mixes and take a water bottle. That way you can mix your own drinks so you don't go broke buying them past security.
6. The car seat might help a bit with familiariity. You might take an airplane book with you so you can show him the different things that will happen on the plane and than take that book with you to show the same things.... Pilot, flight attendant, luggage, etc. They had some really cute ones at Borders.
I would not suggest Benadryl as it has the upper affect on some kids and this is a new situation so probably not a great thing to do. One thing that I have used in the past is Planetary Remedies, "Calm Child". It is an herbal supplement that my son has always responded well too. Each child is different, but I would not recommend Benadryl (as a previous pediatric nurse and mother!)...
Don't work yourself into a stressed out state either. Just take deep breaths and know that this will be another learning opportunity for you and your child. If you remain calm it will help your son. Even if the day starts off a bit turbulent or whatever just keep breathing! Your child will be able to sense if you are stressed and since this is a new situation he will be looking to you for those indicators.
I was nervous the first time we flew with our son too but it ended up being a great trip and we have had many since then.
Let us all know how it goes!