OK . . . I'll put in a vote for Crazy . . . but with a caveat . . . you're not crazy for wanting to provide protection for your family, but honestly putting smoke detectors in certain places is not wise . . . as Be Green found out since every time you burn the toast, have a small spill in the oven, etc. you'll have the detector or detectors going off.
Honest opinion . . . since I really truly can say I am an expert at this since I am a certified Fire and Life Safey Education Officer in my full time job . . . take others advice and spread out your detectors. Nix the one in the kitchen . . . even if it is in the room with the woodstove. Instead make sure there is at least one on every level of the house (including the basement), in the hallway outside the bedroom and in the bedrooms.
As I said there are some bad places to put smoke detectors as you may have false alarms . . . and the problem with false alarms is after a while people get used to hearing them and no longer react to them. Bad places for smoke detectors include kitchens, bathrooms (steam can set them off), laundry rooms (humdity and dust), attics (the temp fluctuations of going from very cold temps to very hot temps plays havoc with them) and garages (nuisance alarms from car exhaust) are places where smoke detectors are typically not recommended. That said, sometimes going with a detector such as a photo-electric detector in one of these areas can reduce the likelihood of a false alarm if you insist on putting one in such a location (and truthfully I have one in my laundryroom -- a PE type -- since it is also near my oil boiler -- and I have had very few issues.)
So I really would not place a detector in the kitchen . . . and truthfully in my own home I also do not have a detector in the same room with the woodstove . . . to reduce the chances of a false alarm from any smoke infiltration. That said . . . I would not have an issue if someone was concerned enough and wanted to put a detector in the same room . . . providing it is not too close to the stove. In my own home . . . there are two detectors in the two adjoining rooms so if there ever was an issue one or both would be activated fairly quickly.
If you really insist on having some sort of detector in the kitchen you may want to investigate the price of a heat detector. Some folks install these -- albeit they are rare for residential use -- in kitchens. These activate by either going off at a pre-set temp or when the temp in the room increases by X degrees in Y amount of time . . . some people do not consider these as good as smoke detectors though since they tend to activate after smoke detectors go off . . . but my own feeling is they don't hurt and if folks sleep better at night . . . well . . . they can't be a bad thing then.
Incidentally, in case anyone is curious . . . leading causes of fires in the US. Cooking, Heating Equipment and Electrical. I only mention this since technically electrical fires could break out in nearly any room.
Final thoughts . . . since you have a youngling that cannot get out by themselves I would recommend sleeping with the child in your room or in a room very close to yours . . . as the child grows older you may also want to look at some of the newer voice-alarms . . . they've done some studies and found that some children do not wake up to the sound of a traditional smoke detector, but when voice alarms are used that use verbal warnings -- either pre-programmed or even recorded by the parent -- the child wakes up.
Feel free to ask any other questions . . . I'm crazy about fire safety.