The parser by itself is not enough. As you say, you need meta-data with the column information for the tables. And the process will include disambiguating partially qualified table names in the FROM
list based on the default schema.
For a working example of code that does this using the parser, look at the open source akiban-server SQL engine. Specifically, at AISBinder.expandAllsAndNameColumns (https://github.com/akiban/akiban-server/blob/master/src/main/java/com/akiban/sql/optimizer/AISBinder.java#L793
Note that if derived tables (subselects) might occur in the FROM list, it's possible that you will need to do the whole thing recursively.