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In a natural form of cod liver oil, with natural vitamins, the A & D work synergistically and you'd have to take an awful lot for it to be dangerous. A maintenance dose for a child would be about 1/4 tsp per day, but in this case you could give up to 1/2 tsp for a while. I'm more inclined to think that the omega 3's can be overdosed on if too much is taken over a long period.

Green Pasture check regularly for contamination. Somebody else brought up the so-called scandal in another comment, which I will address in answer to that comment (so you won't see it come up in your replies)

It can be toxic, especially commercial cod liver oil because its heated and artificially cleaned. With fermented cod liver oil maybe bit diffferent, its more safe but taking excess of cod liver oil may lead to overdose for vitamin D and children are way more sensitive than adults. same for Vitamin A, it also high amounts of A in cod liver oil and overdose for A can be serious for children.
Dont mean to scare you thats why I think its smart to consult doctor to see what doses are good for certain age.
I personally take Omega 3 but I try to stay away of Cod liver oil just because nature of it, i.e. extracted from fish liver, Im not sure about all the toxins getting with oil. I do take at least 3g of high strenght Fish oil daily so I do support of taking it daily as its necessary, just not a fan of cod liver oil.