My DS2 is much the same age and though not as far as I know allergic has to be treated as such until futher notice as his brother was allergic to egg, milk and nuts. We have similar problems, he is a skinny little chap.
With my eldest's nut allergy, I was never going to risk giving him any nuts in case he became allergic to those too, so personally I would not try other nut butters (DS1 is allergic to peanuts, cashews and almonds I think.)
What about biscuits instead of rice cakes as snacks? Lots of biscuits are fine for egg/milk/nut allergy sufferers, unless you are having to avoid everything that may contain traces of nuts (we were told not to worry about products with this on unless DS1 actually reacted to them). And as we all know they have quite a few calories!
All bourbons and ginger nuts seem to be ok, many Rich Tea biscuits seem to be ok but not all (McVities's are NOT ok).
THere are some soya chocolate puddings in the special section which are nice, though DS1 would never eat them.
I used to buy the dairy free chocolate and make crispy cakes with them, although I shudder at giving something messy like that to DS2.
You can make a decent cake without eggs would you believe. I do have a recipe but there was one on here further down the page which looks good too.
Pure spread can be mashed into mashed potatoes, make into garlic or herb bread.
As for protein, we always think of meat but there is protein in bread too.
Will post again if I can think of anything else but the egg/milk free diet does tend to be rather low calorie and your DD will probably just be skinny.
BTW make a food diary before your dietitian's appointment. Our paediatric dietitian was able to put DS1's diet into their computer and work out whether or not he was getting enough of everything in his diet - I was so worried. Even if they don't offer to do that for your DD, there's a good chance that they will ask you to do one.