We gave him rice milk at 18 months old, and he continues to drink it today. We didn't take Morgan off the soy milk until he was 18 months old however. This was probably pushing his immune system over the edge, especially since as a baby, his main nutrition was from the soy milk. It has been suggested that persons allergic to soy might be able to tolerate soy oil. In your child's case, this may or may not be true.
Some people do have serious reactions to soy oil also.
Read food labels is a necessity for a Soy Allergic child Avoid anything that has 'soy' or 'lecithin' listed in the ingredients. This could include soybeans, soy protein, soy sauce, and soybeans. And as with peanut oil, some children can tolerate soy oil and others can't. I'd err on the side of caution and not use soy oil. Soy protein may be present in an ingredient such as vegetable protein or natural flavoring.