Hi E. -
I've traveled a lot with my (now) 5 year old by myself - we've gone cross country and to Europe and I didn't have any problems and she didn't either! A couple of times someone would say that they didn't even know there was a 2 year old on the plane near them.
I think if you set certain expectations from the get-go, you'll have an easier go of it. We expect our little ones to be in their seat and buckled or on our laps the entire flight. No standing, no kneeling, etc. And absolutely no kicking or yelling. We practiced airplane voices for a while before going.
The other thing that took me a little longer to figure out is that I was not going to get to read, listen to my music, chill, etc. as long as she was awake. Once I gave in to that (I say that because I really struggled with this!) and decided to just be her amusement, it was all good.
If you're travelling out of Tampa Int'l, they are usually really helpful in security - they will often let you skip lines and give you a slower line to let you fold up a stroller, take off shoes, etc.
Have a lot of fun!!! I think travelling with little ones teaches them how to travel and appreciate the opportunities available to them!
C.