How can I get my server's uptime?

Use the built-in function pg_postmaster_start_time

select current_timestamp - pg_postmaster_start_time() as uptime

More details in the manual: http://www.postgresql.org/docs/current/static/functions-info.html

If you want seconds, use extract:

select extract(epoch from current_timestamp - pg_postmaster_start_time()) as uptime