cant answer all your q's but-
ive been using rice milk as i have soya intolerance as well as dairy and its great(tastes ok in tea as hate soya and goats urggh !)
can buy most of these in a large supermarket now
i dont think cheese would be advisable but yoghurt maybe ok as sometimes a dairy allergy/intolerance is to do with lactose(a substance in milk) which is broken down in yoghurt and therefore not a problem
i would imagine if it works you would see results in about a month or less
if your dd has eczema i would strongly recommend that you cut tomatoes out of her diet as they are very irritating to eczema (something to do with them being from the deadly nightshade family of plants) . i have eczema on one hand and if i cut them up its agony and the last time i ate them in a homemade tomato sauce i woke up in the night scrathing cause my eczema was burning
also avoid nuts peanuts
other things to look at(google/internet ) would salicilates (asprin like substances in foods/fruit/veg eg apples, that can cause allergic reactions )
vega food testing - this is poo-pooed (scuse my terminology by some but i have known people for who/whom it has worked well
dont know if she will grow out of it you cant really say or know that but i would suspect not fully although it probably will get better
ps i once got a blood test for food allergies by my gp which was very accurate but not all gp's can/will give these
also franch what bath products do you use on her skin many leading commercial brands are full of chemical skin irritants (johmsons for one ) try a company called neways.co.uk they now have a site where you can buy the prducts direct (im an agent for them) if you pay £5 you will get a third off the onscreen price of the products theyre not the cheapest but because thyre good they last well and so are worth it (all their products are more than excellent-food suppliments(esp.maximol and hawaiian noni juice!) toliteries etc)
well blow me i think i have given an answer to nearly all your q's pls scuse any spelling mistakes
best of luck franch hope your dd's eczema gets better