When my child was one, he ate anything that I ate. I don't see any reason a 1 year old can not have black beans. I fthey are really salty, maybe just small quantites.
Black bean is nutritious. I served this to my daughter occassionally when she was one. I cooked it real soft and then pureed. Lentil bean is also good. If she refuses milk, try make your own organic soy milk.