moving large PostgreSQL/PostGIS database
I would recommend dumping the 9.1 database from your new 9.3 server like this:

pg_dump -h remoteserver -U remoteuser remotedbname -Fc -f my_old_server_backup.dump


I recommend using the 9.3 pg_dump as pg_dump is always backwards compatible, but not forward compatible. In other words, the newer pg_dump will take care of any syntax changes that the new server requires that the older utility doesn't know about. 

Be sure to make sure your pg_hba.conf and listen_addresses in postgresql.conf are set up to allow you to remotely connect and dump appropriately as well.

If you wanted to try a dump and restore in one step, you could try this as well:

pg_dump -h remotehost -U remoteuser remotedbname | psql -U localuser localdbname


Hope that helps. =)