Benadryl dries out my sinuses which is not what you want to do on a long flight. My sleep aid of choice for long haul flights is booze and melatonin. I'll have a drink or two before boarding the flight, and a couple glasses of wine with the dinner service. Watch a movie or show until my eyes are heavy, and then put in earplugs and a mask over the eyes.
Anyway, a trip to Australia (and preferably New Zealand too) should be on everyone's bucket list. I lived in Sydney for a few years and I miss it badly.
Most people I talk to about it are scared of the flight, but it's never as bad as people think. When I lived in Sydney, I took 7 or 8 trips back and forth to the US to see family or friends. I flew a few different airlines and I would recommend Qantas. They're usually not the cheapest, but they have decent customer service and fly the A380. An overnight flight to Australia departing LAX or SFO or DFW in the late evening would pass quicker and more comfortably than a cross-country flight from Boston to LA. Going back the other way is a bit rougher though, since the long leg departs in the middle of the afternoon.
Qantas allows (or at least did allow) you to pay a little extra for an exit row seat, which was well worth it on the A380. On the other hand, Premium Economy is not. Because of my status (due to frequent business travel to Europe), Qantas would sometimes bump me into Premium Economy when I had booked an Economy class ticket for personal travel. You get better food and wine and a little more recline, but it's not worth paying double.