This is always a difficult issue to be certain of online.
As a specific example, I know the CP The City has double-double rooms that accommodate 4 for a modest premium. It can be good value at times (mainly weekends) as the location is in the business district but still pretty central.
On the otherhand I webchatted about this with IHG recently. They basically told me I could book for 2+1 and the baby doesn't count; just note it in the reservation. I was asking about a specific hotel (in China) but the answer was very rapid/generic, not a case of them having reviewed the hotel's own policies.
I would maybe do a search for 2+1 and then called up your preferred hotels to see what they can do. To boost your comfort a little further I would also request a crib/cot if possible and see was size you get: our 3yr old isn't small yet still often manages to sleep in a crib "officially" supplied for our infant.