My friend bought a pony for her 5 year old, and when she had the vet check, there was a history of laminitis. The vet told her, "There are two kinds of ponies: those that have foundered and those that will founder." She went ahead and bought the pony and never had a moment's problem with her. Of course, she was very careful and took good care of the pony.
I bought my daughter a large pony that I could ride when my daughter was 3. I mostly rode the pony until she was 5 and could ride on her own. My daughter was not all that interested in horses, but rode with me because it was something fun to do with Mom. My daughter is 13 now, just finished starting her own filly that we got when the filly was 4 months old. She is a beautiful rider and handles the young filly perfectly. She still isn't all that interested in horses, but she has a great time riding with her friends. Horses gave her a lot of confidence. Just because she doesn't have the passion I have did not mean that having a pony, and now a horse, did not help her quite a lot.
I would have the vet check the seriousness of the laminitis, but not rule the pony out. And, in my opinion, kids don't need to have the total passion for horses to still benefit from having one. By the way, we call our pony The World's Greatest Pony. He is marvelous.