Hi apk, be very VERY carefull, the Thia's use peanuts or peanut oil in their cooking to a very large extent. suggest you eat nothing which you have not seen prepared and buy nothing which does not have a ingredients list for you to check out. Even things you don't expect might have the oil or traces of nuts in it. We had a visiting tourist died here (Not Thialand by the way) after having a pizza which had traces of nut oil.
Get a laminated card printed with " my child has a severe peanut allergy and must not eat any food that has been in contact with peanut or peanut oil.....etc" in Thai and other languages that you are likely to need.
My friend had a severe reaction to a bowl of pasta and sauce when we were in spain, i don't think the waiter or chef understood when we asked if it had nuts in. we should have asked if it was possible any nuts or nut traces could have come into contact with the food being cooked for her, be very very careful.
One suggestion only: FORGET IT. No parent with any love for their child would consider Thailand, of all places, with only a slight peanut allergy but a severe allergy. Is this just a sick joke?