[Pitchwife]

Welcome to the Downs, almiel! As we don't have a special language forum, I'd say this is a good place to post your question.

hína i Eä is fine for "child of the universe" as far as the meaning goes, but Quenya being an inflecting language (unlike Sindarin), you'd have to stick the appropriate case ending to Eä*; for the genitive, this would be -o, giving Eäo, which however looks/sounds horribly awkward with its three vowels in a row (not that it's wrong, it's just a matter of phonaesthetic taste).

Also, Tolkien tends to use Eä as a sort of proper name of the universe, without the article, so I'd drop the i, leaving hína Eäo; but if you'd like to avoid the three-vowel-cluster, your compound Eähin (modelled on Eruhin) actually seems like a good alternative to me.
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*(especially because eä can also mean "it is" in the sense of "it exists", and i can also be the relative pronoun, so hína i eä could be misread as "a child that exists".)