Hi - Welcome to FlyerTalk - I am surprised your username hasn't been used already!
We have used a BabyZen with Master LavaJava for his last 14 flights and it works very well. The bag is a must in my opinion but I don't think it's the only suitable stroller, especially as it's quite expensive. When shopping for the Zen I looked at the GB Pockit which is smaller, but doesn't feel as sturdy.
I would also say the Zen is about the largest you should go, for overhead bins.
EDIT: I like the look of the Ant, especially the ability to use like a wheelie bag. Look like it's within limits for carry on.