Well, basically you tell rsyslog what type of events to log and to where, then you can forward your logs at the bottom of the conf file to a remote host.
You can use bash expansion with $(date %h-%d-%y) or however you want to set it, into the file name itself.
You can then add the following into the forwarding rule section:
Replace the 10.0.0.1 with your IP and the 80 with the port. Looks like 514 in this case.