Congratulations!

Its been a while as ours is no longer a toddler, but my input:

1. Get one of those folding buggies that can fold into a ridiculously small size, put in a bag and in the overhead compartment rather than checking at the gate. 2 year olds can be heavy to carry if they don't want to walk and this can be a lifesaver. There are a few brands available.
2. Change of clothes for you and you littl'un. (dont underestimate the amount of vomit that can be produced at altitude!)
3. Extra seat as others have already said.
4. Tantrums/crying usually stop when the plane starts moving. Sleep usually follows.
5. Milk/drink on take off/descending (helps regulate ear pressure).
6. Wet wipes
7. Food, drinks, snacks.
8. Dont stress. Most other passengers wont have an issue with a crying child if they can see parents are trying to do something about it.