Newsprint ink used to be toxic but at a level where your child would have to chug back neat ink or work through WH Smiths' entire stock of newspapers before you needed to worry. Now IIRC most are printed using non-toxic ink. So probably the one your DD ate was non-toxic, and if not the "chugging back neat ink" thing still applies.
They used to wrap fish and chips in it for years. Anything dangerous would have soaked into all the vinegar and hot fat, so it must be OK. Newsprint used to contain arsenic but that was over a century ago, I think!