Dealing with partitioned tables in Postgresql
Let's quickly check the COPY documentation:


COPY { table_name [ ( column_name [, ...] ) ] | ( query ) }
    TO { 'filename' ...}
    ...



Your friend will be the query part.  It means that you cannot only copy from a table, but also an arbitrary query.  And example can be:

COPY (SELECT * FROM ONLY your_table) TO '/path/to/dump.sql';


Notes:


you have to specify an absolute path with COPY
it is usually handier to use \copy from psql as it copies the dump to the client machine, not the server.  In your case this may be irrelevant.
in practice, keeping daily tables is usually too fine-grained.  If all your queries can use constraint exclusion, then it might be all good, otherwise you might notice some planning overhead.