MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

EDIT: I have been asked in a comment what a filtered quasi-isomorphism of DG-coalgebras is, so let me add an explanation of this to the answer. This notion does not presume a fixed filtration on a DG-coalgebra, but rather a class of admissible filtrations. We consider coaugmented DG-coalgebras, i.e., the basic field $k$ is embedded as a subcoalgebra into a DG-coalgebra $C$ and its image is annihilated by the differential. An increasing filtration $F$ on $C$ is admissible if $F_0C=0$, $F_1C=k$, the components $F_iC$ are preserved by the differential, and the filtration $F$ is compatible with the comultiplication.
I know, basically, two answers to this question. The first one starts from the observation that what you call "a relatively easy theorem" generalizes to infinite-dimensional Lie algebras $L$ by replacing the exterior algebra generated by $L^\ast$ with the exterior coalgebra cogenerated by $L$. Then the construction becomes covariant, but produces a (conilpotent) DG-coalgebra rather than a DG-algebra.