The toddler is only one and would be lap held so I wondered what most people do in this situation?
I would ask myself in an emergency would I have the strength to hold my child pinned to the floor. That is the standard for lap children in an emergency landing situation. Which while rare can happen on any flight. Look up United Flight 232 which had a major problem 1 slightly over 1 hour and 15 minutes into a flight that was about 2 and a half hours that ended up with a crash emergency landing. 1 of the 4 lap children was lost in this landing.
While you could luck out and have an empty seat next to you and be able to sit a 1 year old in that seat I would personally spend a little bit more and purchase a seat for my child. For a 1 year old since the newest recommendation from the American Academy of Pediatrics is to keep them rear facing at least until age 2 and then as long as possible based on the weight and height limits of the seat. My oldest is 14 and a half and there was a parent grassroots movement to keep our children rear facing until they out grew their seats in the rear facing position that started about the time she turned 1 year old. As a result she rear faced until 28 months and her now 11 and a half year old sister (who has always been taller compared to the same age) until 26 months of age both of them out growing the seat in height. (Weight wise they could have rear faced until close to 4 for my teenager and well into grade school for my preteen).
As long as the carseat has a sticker on the side saying that it is accepted by the FAA you can fly with it in the United States as well as in most other countries. The sticker will be in the same location as the the one stating it is accepted for automobile use. The only restrictions are that unless there is a 2nd aisle no one not even the parent can be between the seat and the aisle so you must place the child against the window and you will need to sit in the middle seat next to your child. Most airlines will allow you to board early in order to position your seat. If you rearface and your child kicks they are just kicking their own seat and not someone else in the back (though someone may be upset that their tray table is moving). Rear facing will also allow your child to face you so you can easily hand small toys or even play games like peak a boo and patty cake.
From experience I can tell you staying at a Disney resort and using Magical Express traveling with a carseat is really easy. My toddler's carseat was loaded on the bus along with our carry on luggage from our flight. When we got to CBR Bell Services not only loaded us and our luggage into one of their vans to take us to our island they assisted my DH in installing the seat properly. We were planning on just having the seat in our room against the wall but were pleasantly surprised when Bell
Services offered to store it for us. When we needed it for going off property the day we went to Sea World my husband took the internal bus over and got the seat which we installed in the rental car we had for the day. When we returned he took it back over to Bell services who had it securely installed in the van that came and picked us up at 3:30 AM the day that we left in order for us to get on the 4 AM Magical Express bus to MCO for a 7 am flight.
We did gate check the seat on the plane but it was nice to have the seat strapped to a luggage rack (using bungee cords) to put our 27.5 month old in to get through the airports especially since we had a layover in Salt Lake (Yes we did allow some running around to get the wiggles out but we were able to decide when and where for our peace of mind and our child's safely and used an out of the way corner close to our gate area before boarding the 2nd flight.
The best advice I was given before flying with my children came from an online friend of mine who is a former flight attendant on 2 different airlines who as an expat living in Europe and flying back and forth to visit family in the United States many times a year with her own children. She has a blog on blogspot called flying with children. Some of it is not going to apply but she talks about everything from getting that passport photo to handling a bathroom visit on the plane including diaper changes.