S.,
My seven-year old daughter has had a peanut allergy for four years. We have seen several allergists, including, most recently, the food allergy experts at Johns Hopkins in Baltimore.
They all say to avoid ALL nuts because there is a greater likelihood of developing allergies to other nuts besides peanut (which my daughter actually eventually developed). They advise staying away from anything that is processed in a facility with peanuts or that says "may contain traces of peanuts" because there is between a 10 to 30 percent chance of cross-contamination from something that was made on the same machine using peanuts.
Be very careful about reading ingredients in everything. Don't rely on the allergy statements at the bottom of a package because several times I have found peanut or peanut flour is an ingredidient but it is not highlighted at the bottom of an ingredient list as is required by law.
Also, read EVERYTHING, even if you don't think it contains peanut. I gave my daughter cheese ritz bits a few years ago, before I started reading everything routinely. It turns out that they contained peanut flour. Alot of cookies and bake and break cookie mixes contain peanut flour.
Also, avoid bakeries and bake sales and baked goods, because "if you can't read it, you can't eat it." That's the rule we have in our house. Again, the issues are possible hidden ingredients and the risk of cross-contamination. A boy at my daughter's old preschool had a very serious anaphalactic reaction when she relied on a waiter to know whether a baked dessert had nuts in it.
If you go to ice cream parlors, ask that they use a clean scoop, and scan the area for loose peanuts. I have my daughter avoid the messier ice cream parlors where peanuts are spilled all over the place. It is better now that she is older and can tell me if she thinks there is something in her ice cream, but with a toddler it is more difficult.
Maybe you have heard of FAAN, the Food Allergy and Anaphalaxis Network, based in Virginia. They have tons of helpful info on their website.
The bottom line is that it can be a scary allergy, and one to take very seriously. I wish I had realized this right away with my daughter. Unfortunately, our first allergist gave us very little info, and I didn't develop strict habits right away.
It is impossible to know whether a reaction will be severe or not because it depends on how much peanut is ingested. People always ask whether my daughter's allergy is severe and I always say "yes" because it could be.
When your toddler is at a preschool or daycare, make sure the environment is peanut-free. Most preschool environments are very good about that these days.
Hope this helps.