That diet is very extreme, I need to post a revised one soon. Here are some comments though:
1. Milk, if not from goats or sheep, is high in sugar. Looking at the carbohydrate content and compare it to the sugar content. In cow milk it's all the same, the carb content is simply sugar. Goat's milk is slightly better, but all the milk I've seen usually contains some kind of filler like tapioca starch, which I would avoid.
2. Oats are probably the best grain to try, but again, as I've said, many hypoglycemics, especially those just starting their diet, have trouble with grains and find it easier to add later. Your body will adjust eventually, but don't expect to happen quickly.
3. Cheese is okay, that's something I changed, as long as it's not processed. If it just contains milk, culture and maybe a bit of spice depending on type, that's fine. If processed do not eat it. Raw cheese is better for you, but hard to find.
4. Carrots must be avoided. All root vegetables are high in sugar and cause a quick rise in sugar. Potatoes and beets are obviously included in this mix, two of the worst vegetables in the entire world.
5. Cheese would be good at night, but I wouldn't recommend milk because of the sugar content. Could be the problem.