We've eaten out fairly extensively with our little one, who is 10 months. Most restaurants are very accomodating if you go to "local" type places. The La Commensal chain of vegetarian restos is fairly good, the best one being on Ste. Catherine. The Italian places around Marche Jean-Talon are very kid-friendly also. I tend to look for places that are down-home and where locals eat, they tend to be the friendliest.
I get the impression that "unusual" cuisines are out so I won't give you my list of Asian places, which is what we lean to. Let me know if you want them.
Hi ! There is a lot of places where you will be welcome with the kids. For example there are the Saint-Hubert BBQ restaurants, it is a local chain specialised in
chicken. Also Bar-B-Barn with a couple of addresses also with chicken! And for a change there is Giorgio a chain of italian restaurants family oriented. For addresses check in the local yellow pages book.