I can understand your concern for your child's health. Not all vegetables have goitrogens such as cruciferous vegetables like broccoli, cauliflower, cabbage which are known to interfere with thyroid functioning. Since your child is having
hypothyroidism which is a
hormonal problem and not related to
goiter which occurs due to
iodine deficiency, you can give these vegetables safely. Other vegetables like green leafy vegetables like spinach, fenugreek leaves, gourds, ladiesfinger etc to name a few can be given without any hesitation. Include plenty of fresh fruits and raw vegetables as salads in his diet, whole grain cereals like oats, oat bran, whole wheat products, wheat bran, brown rice etc can be given.
Prefer low fat or skimmed milk over full cream milk. You can also give curd and home made cheese for calcium and
proteins.
If non-vegetarian, include lean meat, chicken without skin, egg white (egg yolk is rich in
cholesterol, so it should be avoided), fish as sources of good quality proteins.
Avoid fats from butter, ghee and margarine. Cut down on the intake of salt to reduce blood pressure. Use less oil for cooking and avoid oily and rich gravies. Avoid giving junk food, processed foods which will only increase calories from fats and sugary drinks/fizzy drinks.
Make sure he is active and limit sedentary pursuits such as watching TV for long hours, sitting on the computer.