Your under age 2 toddler needs essential fatty acids both for growth (adequate calories) and for development of his brain and nervous system. Many food sources of fat have cholesterol, which is a very important part of a baby's diet. Unfortunately, our culture has made cholesterol a bad word. Realize, though, that breast milk is over 50% fat (in the form of cholesterol), and breast fed babies are less likely to have elevated cholesterol levels as adults. Also, it is recommended that you not limit a child's fat intake until age 2 (This is for normal weight children. There are cases of toddler obesity in which these quidelines do not apply).
Since your child has exzema, you want to be cautious of foods that are potential allergens. Peanuts and peanut butter, eggs, dairy are common culprits. For this reason, almond butter-mentioned in an earlier answer, may be a very good option. Also, intake of omega 3 oils has been associated with reducing allergies. (I did not search out more on that topic, but it might be interesting to explore further)
In figuring out how much food your toddler needs, pediatricians usually advise 40 calories per inch of height. This should be a general guideline.
In addition to carbs and proteins, give your baby a variety of healthy fat-containing foods. Omega 3 foods include safflower oil, flax seed oil, walnuts (grind them up and sprinkle in his food), fish (esp. oily fish like salmon). Make sure any oil you buy is cold pressed, to preserve the health benefits of the omega-3; Some food ideas: add a teaspoon of flax seed oil and/or ground up walnuts to cooked cereal; saute veggies in canola or safflower oil; small bits of fish (make sure all bones are out), or poultry; smoothies with flax oil (especially since he likes yogurt). Lastly, Nordic Naturals makes a gummy bear type chew that is an EFA supplement. I have no idea how these taste. There might be other companies that also make a child-sized EFA supplement.
Good luck!

If you go to speicalty stores they do have things like Goats Milk, Camel Butter, ect. I have actually heard that they are better then cows milk and much sweeter (I would assume fat has something to do with the sweetness)*Edit from reading I found it has to do with what they eat, will change the taste*

http://www.reuters.com/article/oddlyEnoughNews/idUSTRE56K4YZ20090721

Says that "Camel milk contains five times more vitamin C than cow milk, less fat, less lactose and more insulin".

http://www.saanendoah.com/comapre.html shows the difference between Human, Cow and Goat milk.

Have you looked into wild salmon oil? It's a great source of omega 3 fatty acids (EPA and DHA).

Try almond milk..it is a great alternative!!!

If there are no nut allergies, natural peanut butter and other nut butters, in moderation, also have a lot of healthy fats, and of course peanut butter is a common kid staple. Remphasize the *natural* part, meaning none of the stuff that's blended with hydroginated oil. These will have a layer of oil floating on top - if you refrigerate the jar after stiring it will stay incorporated. The only ingredients on the label should be peanuts and optionaly salt (you can get salt free but I think the salt is important for taste). There's not usualy sugar in these either; if you want to sweeten it you can stir in a little honey (note: never feed honey to kids under 1 year old) or agave syrup (granulated sugar is just harder to mix in).

Jiff came out with a "natural" peanut butter that's smooth and sweetened, but they use palm oil, which is high in saturated fat and argueably not much better than hydroginated fat.