I would NOT do benadryl. Especially not if you do not know how your child recats to it. My daughter was precribed benadryl at 8 months for a rash. She would fall asleep quickly on it, sleep very deeply for four hours and as soon as it wore off, she woke up drugged and drowsy and in a terrible mood. It was hard enough to deal with this at home, I would NOT want to deal with it on a plane!
I have been taking my daughter to Europe by myself several times since she was 3.5 months old. Let's face it flying isn't fun for anybody, but we survived!
Since a 12 hours flight sounds like it will be international, call your airline and ask for a bassinet seat. They are lifesavers when travelling with little ones!
Take plenty of snacks and toys, prepare for nusing a lot (or bring bottles if not breastfeeding) and don't forget extra snacks and drinks for yourself.
At 7/8 months flying was still pretty easy for us. Yes, there was an hour of screaming here and there (but being honest even I want to scream after sitting on a plane for a few hours). Bring a carrier or wrap so you can easily carry your baby up and down the aisle. Also learn how to operate it alone (put baby in an out) and practice using the bathroom with baby strapped to you.
Since international flights have early check-ins, bring a blanket and some toys, so baby can move freely and play in the airport. This is also great if you have a layover or delays.
I like to get gallon sized ziploc bags and put everything in bags and then in my carry on (bottles in one bag, finger food in another, jarred food in another, pacifiers, toys... you get the idea) that way to don't have to dig through all of the stuff in your bag and stuff it back in when you found what you need.
Last but not least:
If you have an option, pay the extra $$$ for a better airline. It's worth it!
And ask for help when you need it. I found that flight attendants were very helpful with holding/watching my daughter for a few minutes while I was using the bathroom, bring me things and helping me with my carry ons.
Good luck!