Nope. Peanut allergy isn't always automatically severe (BUT it CAN be, which is why all the hysteria). Any reaction to any allergen can be immediate or delayed for even days. Biphasic reactions are when there's both an immediate and a delayed reaction.
When someone develops an allergy, there needs to be prior exposure somehow where the immune system has identified the allergen as such. My son's very first time eating green beans brought on a systematic reaction, but it wasn't his first ever exposure because I'd eaten them while breastfeeding, for example. I've never, ever fed him nuts but he'd go on nursing strike when I ate anything that had nuts in it, etc. He has multiple food allergies and the symptoms of each food range from digestive troubles, to hives & rashes, respitory problems, and anaphylaxis. My little brother, on the other hand, literally lives on peanut butter and has been eating it since he could hold his own spoon with never a problem.
So... I'm not an expert either, but this is something I have experience with.
The theory for waiting until age 3-5 to introduce peanuts isn't to prevent allergies, because it's my understanding that you're either susceptible or you're not. The wait is because a) choking hazard and b) so the child is old enough to describe any weird feeling that may signal an allergic reaction.
My advice would be:
Don't freak out. Hard to do, I know, because just the thought of a reaction can be terrifying. But keep an eye on her and maybe jot down anything that concerns you and the time it happens, just in case.
Signs to look for are hives (can be any size, or move around, or disappear and come back-- they go away with benadryl), any kind of unexplained itching or rash (in my son's case this happens within 5 minutes to an hour of exposure), sudden runny nose or wheezing, hoarsenss of voice, vomitting or explosive poops soon after exposure, unconsciousness and drop in blood pressure.
The mamas on the Health & Healing board have a subcategory devoted to allergies, if you're very worried check there. Sometimes I find that knowing more about something makes it less scary.