I was digging archives to see anyone worked on supporting domain's over composite type and found your patch, but that was pulled back. According to commitfest comments it needs some more work...
typecmds.c says: "Domains over composite types might be made to work in the future, but not today."
Attached is a patch that allows domains over composite types, together with test cases in domaincomp.sql. A domain over a composite type has typtype TYPTYPE_DOMAIN, but typrelid and typrelkind are empty: that information is only available in the pg_type record of the base type. The remainder of the patch follows from that choice. While parsing a record expression into a row type, an extra coercion node had to be inserted to ensure that the domain checks are called.
All regression tests are ok, comments are highly appreciated.
