Before I had my youngest, I flew with Jet blue and two kids (with their own paid seats!) and carried on their booster seats.
But this was almost 7 years ago. Even if you can't use the booster on the plane, you can have them stow it in the overhead as a carry-on. Think of it as one of your child's carry on items. Most airlines allow two carry ons per person. And even if they are going to allow only one... think of it as a stroller and have them stash it somewhere on the cabin for you like they would for those that have strollers.
I did however use booster seats (weren't backless) for my other two when they were real small when we flew. I was able to strap the booster into the airplane seat and then strapped the kids into the booster. I can't say enough about how nice the Jet Blue crew was for that. They all understood and were even helpful about helping the three of us on and off the plane.
Best of Luck and happy travels!