I'm pretty sure you can't use a booster seat on the plane.
Aside from that, I have no issue with lap babies or flying without car seats. The risk is soooooo low that anything would happen on a plane. Yes, it is technically safer to have a child in its car seat on the plane, but the risk is so low, I don't have an issue with it.
However, I am against renting car seats or checking car seats. I wouldn't trust a rental car seat, and would worry about how a car seat would be handled if checked. I have flown many times with my kids. We've gone to Disney a couple times. With lap babies and toddlers. Neither had car seats, but we didn't need them at the destination either. I've also flown to locations where I did need car seats at the final destination. In those cases, my child above the age of 2 sat in his car seat on the plane (to protect the seat, I wasn't worried about him). I had a lap baby but on almost all the legs of the flights I was able to get a free seat for him since one was available. In those cases he sat in his car seat on the plane to protect the car seat. In one instance there was not a seat available so I gate checked the seat. Luckily, that seat we brought for him was really just a back up seat, and not used everyday with him at home.
As long as your child is 40lbs, they are within the weight range for the lap belt on the plane to be an adequate restraint. I personally don't like the harness for flying that the pp linked. I feel it pulls the lap belt up onto the abdomen. And unlike what the pp thinks, the lap belt on the plane is a "restraint". It is not flying without restraint to use it unless you don't buckle, which is illegal.
Yeah 40 lbs is technically the range for just using the belt, but had my 40lb not quite 5 year old on a plane a few months ago and that belt totally didn't fit....
Last time I flew with my daughter she was just over 2 yo. I brought the CARES harness and I don't feel it fit her really well, but it was better than nothing. It was just me and her and bringing a convertible car seat just wasn't realistic, unless I somehow turned it into a stroller, but then I wouldn't have had a stroller when at my destination. IDK, mine may not have been the safest approach, but like someone said upthread, the risk of something happening with air travel is so darn small. We bought a new car seat and shipped it to the family members meeting us on the other end.
I would use a car seat, especially if you will need one at your destination. It's just so much easier to keep them contained on the plane plus gives you extra safety. You can bring a seat and a stroller too, as long as you choose a nice light travel seat. We normally prop it up on the stroller handle with our handles under and push it along that way. Other carry on necessities go in a backpack, which I prefer anyway cause then I have my hands if I need them for DD.