it all depends what exactly your GP wants you to cut out.
With dairy, do they suspect milk protein allergy or lactose intolerance?
With wheat, is it wheat allergy or coeliac disease?
OR, are they not telling you/don't know themselves at this stage?
My mum's a paediatrician and this is her advice. If you suspect lactose intolerance, it's often safe to eat fermented dairy (cheese, although may be best to avoid very soft "milky" cheeses, sour cream, yoghurt - home made is safer than commercial) and butter. To make fermented dairy, lactobacilli consume lactose and turn milk sour so the end product contains very little lactose, if any. Butter is almost entirely made of fat and likewise will only have trace quantities of lactose (which is a sugar). Only people with very severe lactose intolerance will react to the trace quantities in butter and fermented dairy.
I suppose one way to rule out lactose intolerance is to try lactase enzyme supplements. Lactase is what our bodies produce to break down lactose.
Milk protein allergy: depends which protein. If it's casein, most dairy is off limits. However certain other milk proteins get fully or partially denatured during fermentation, so some milk protein allergy sufferers will tolerate fermented dairy - as above. Again, butter should be fairly safe unless the allergy is severe. Maybe even small quantities of double/whipping cream as that's about 50% fat, too.
Wheat vs coeliac: if you suspect coeliac disease remember you must exclude not only wheat but also rye and barley. Many breakfast cereals contain malt barley extract, and whether or not they are safe apparently depends on the quantity, see here shame they won't give you access to that foods list unless you have a confirmed diagnosis! Also many breakfast cereals (and porridge oats) are made in the same mills as wheat, so will be cross-contaminated with wheat/gluten. So you'll have to look for gluten-free. Which are like 2-4 times as expensive 
There are home testing kits for coeliac disease, so you could try and rule that one out, BUT they are expensive - cheapest I found online was £15 + £2 delivery. Boots do one for £20.50 but I got one last weekend and it turned out dodgy - I recently posted about that in this topic. On the whole these diy kits are meant to be fairly reliable tho, chances are I just had bad luck 
So, this is what I'd suggest: dairy free run - your DS should be ok with butter and possibly small amounts of fermented dairy. How about breakfast cereals with juice, or large chunks of juicy fruit, e.g. citrus (grapefruit works well), watermelon, berries, etc. Toast? Fry-up? Tinned sweetcorn, heated with butter - DS would kill for! Maybe porridge, cook with water and add just a spoonful of double cream? And yes lots of fruit/berries or jam. I use frozen berries to cool it down.
Wheat/gluten free run: yoghurt! Maybe some gluten-free muesli /granola to go with it. Gluten-free porridge. If you're adventurous 
try cooking other grains in the same way as porridge: millet, rice, polenta all work well. Where I come from that's what people have for breakfast - grains cooked with milk, salt and sugar to taste, knob of butter. Fruit or jam for a luxury version :) With polenta, you need it coarse, and either mix with cold water/milk then boil, or whisk as you pour it into hot liquid otherwise it'll go lumpy.
Oh, and I'd suggest you give each diet a couple of weeks as it can take a while for allergens to go out of your DS's system.
Jeez if you're still reading I must have bored you to death 