I think it really depends. Some will let you take a 2.5, some not. My friend (with 2 kids) tried to rent 3.5 room flats and it was roughly fifty-fifty. He ended up with a 3.5 room flat(but its 100 sqm).
There seem to be some unwritten rules, but in this age of child-free people they boil down to number of people per square foot and minimizing apartment wear and tear. There are 2.5 apartments on the market with the surface close to 100m2. This not suitable for such a small family?! It is all about money here.
Try your luck because sharing bedroom with a small child like this is perfectly doable and some landlords are more flexible than the others.
A 2 1/2 year old child does not stay 2 1/2 forever. It is not a question of the size of the apartment, it is about a child having an appropriate place to sleep.
Apartment rents drop a lot when you look outside of Zürich. The OP has not given any indication of his budget but I have helped families with limited rental budgets find suitable housing in the Kt. of Aargau.
I don't know what is meant by your comment "it is all about money here". Do you mean landlords wanting to rent something larger because it means more rent? I don't think this is the case.
No, in places of high demand like Zurich the landlords don't have to. But they still try to get tenants they prefer (and have the full rights to do so). From people owning properties here I heard multiple times that the less people living in an apartment, the less wear and tear, and the better.
Children aren't small forever, but rents aren't forever too. If one can save time on the daily commute and have more energy and time to spend with his/her family, than maybe that's the right trade-off.