Introducing baby to “allergy” foods

My baby has been eating baby food and baby cereal for about a month after getting they okay from her doctor and nutritionist.

We did the cereal for a couple weeks and she didn’t care for it, now she’s mainly eating puréed peas, spinach and green beans twice a day.

She just turned 6 months on Monday and we’ve been given the okay by her nutritionist and our family doctor to slowly start to introduce the common allergy foods like peanuts, fish and eggs.

I didn’t even think to ask how we safely do this. Should we have baby Benadryl on hand just in case?

Has anyone tried or have any thoughts on Ready Set Food?