I've flown a number of times with my LOs at various ages (from 6 months up to 4 yrs). If you can get a separate seat then I would get one as it will provide you with more space and yes, if you can get the car seat on board, then even better and safer. If you can't get the extra seat, usually the flight attendants are good about holding your LO if you need to use the lav or get something from the overhead compartment.
WRT time of flight, I prefer the mid-day flights even if it is during their nap time. As you mention, you won't have to get up super early and usually airports tend to be busier in the mornings and late afternoons (ie. business travel) so you would avoid the crowds, etc. It's hard to predict if you will get a nap or if you do, if it will be a decent one so you just have to be flexible. Perhaps your LO will sleep on the way to the airport or have a nap at your destination.
Is your LO walking? If yes, your DH may spend much of the time walking (assuming no turbulence). Some things to think about when traveling solo is how to pack all of the stuff that's needed when you are on board. I've never taken the car seat on board because I couldn't figure out the logistics of having to carry the seat and push the stroller and then have to carry my LO on board and carry all of the stuff, including the car seat. If you have an infant carrier that you can use, it does free up your hands to carry stuff once you have to leave your stroller on the jetway. Good luck to your DH.
