Ah... ice cream - my eldest's "first solid". She was a little over 3 months old and I was visting my homeland and introducing DH to my favorite ice cream parlor. She was eyeing me enjoying it, so I put a dab on my finger and brought it to her mouth. She then reared back and LUNGED for the bowl... I gave her another finger tip. After that I started he on pureed vegetables and congee.
If you don't want to give your baby ice-cream, don't do it. I don't think my kids actually ate much ice cream until they were almost 3. It's not like ice-cream is a necessity.
As for peanuts, I think I waited until they were over 1 year old and then let them try a bit of peanut butter.
There too, if you are worried, don't give it to your baby ntil you are less worried.