Yes, just like dogs chicken breeds differ in temperament. For a 9 year old to show a bird, it needs to be easy to hold and have good temperament.
Silkies are usually the top recommendation for this but, especially for a first timer, due to the fluffy feathering it can be difficult to point out the body parts when showing at a fair.
Brahmas and Buff Orpingtons, even though they are a very calm breed, are big birds so I can see how they would be difficult for a 9 year old to handle.
Leghorns and Polish are light (~4-5 lbs) and the Polish are very nice looking but they can be/are mostly flighty.
I would suggest getting bantam (dwarf) Cochins. They are very sweet and the hens weigh just two pounds. 4-H kids in my county have had a lot of success showing them. Unfortunately, they don't lay very much and the eggs they do lay are small.
If you aren't looking for anything exotic, then I would then default to getting a Buff Orpington or a Barred Plymouth Rock. They are both calm birds but the downside is that they can weigh 6-7 lbs. However, an upside is that the Barred Rock will give you ~4 eggs a week.
If you are looking at getting a lot of eggs, I suggest getting show birds (ex. Cochins) and production birds (ex. Red Sex-Links). I doubt you'll be able to show sex-links since they technically aren't breeds but they are the best choice for egg laying.
Getting mail order chicks at a day/couple days old is the norm and is cheaper and much less time consuming than hatching yourselves. Some good hatcheries are
McMurray,
Meyers, and
MyPetChicken.