Our DD stopped breathing after licking a tiny bit of peanut butter at 9 mo. Like your family, we all lobed peanuts and ate them all the time so it had never occurred to me about our DD having a peanut allergy too.
Peanuts, like said above, are part of the legume family. However lots of people who have one allergy end up developing other allergies, so just be watch your DS closely, even with foods he has previously been fine with, because just like nelly said, our DD starting reacting to things shed previously been fine with. In fact she had eaten a lot more peanut butter than just licking it four times previously with no reactions.
Unfortunately peanut allergy is the most unpredictable and often the most serious allergic reaction you can have, which is why most of the allergy research goes into peanut allergy. Sorry, I am not trying to scare you, but the first month is a massive learning curve and very daunting and emotional. It is unpredictable is the sense that although your DS has acted this way recently, he can still have a full on anaphylactic reaction to a tiny trace of peanut anytime in the future. You really do need to exclude anything with nuts and that includes may contain nut traces products. And we have no nut containing products in the house from advise from the specialists because even traces of nut in the air from other people having eaten nut containing products can cause a severe reaction. Especially with your DS being so young, they pick up all sorts of the floor etc, I would say it would be safer to avoid anything in the house just in case.
Your GP should really prescribe you with at least 2 epipens because of the how serious peanut reactions can be, even before you have seen the specialist. The waits are often long because there are not many allergy specialists around, and so many people have referrals to them for often non allergy related problems. So it really would make sense to have epipens and piriton on you at all times.
It does get easier once you have worked out what foods are safe, honestly the first months is a nit mare though. We threw away most of our food cupboard, fridge and freezer stock in the first week after our DD's anaphylactic reaction. And the label reading becomes a habit soon enough rather than an emotional never ending battle.
The anaphylaxis campaign website is really helpful, and so are their staff on the helpline. The workshop I found really helpful, especially when it came to our DD starting nursery.
Before finding about DD's other allergies, from just the nut point of view here are some safe toddle friendly snacks; waitrose own brand plain breasts sticks, sainsburys own brand hummus (there are lots so check each one as only one variety is nut free), waitrose own brand hummus, Plum cheese puffs, Heinz biscotti, most rice cakes, and things like fromage frais but be careful with normal yoghurts as even lots of these are packaged in a factory containing nuts.
Good luck and HTH. Mumsnet is a great place for allergy advise though you're in the right place!