Is 10.1.1.1 on the management port? If so, that's not currently supported as TMM needs to use a switch port to send the log messages.
https://devcentral.f5.com/wiki/iRules.log.ashx
log [-noname] [:] .[]
(LTM only) Logs the specified message directly to the specified IP address (and optional alternate port when specified) via UDP. Facility and/or level are required. The iRule name prefixing the message text may optionally suppressed by including the -noname option.
< remote_ip > must be a TMM-routed address. If you must route specific messages to a remote address via the management interface, you must log locally. syslog-ng is able to route messages via both TMM and management interfaces using the standard syntax. You can define an appropriate filter and remote log destination in LTM's syslog-ng service.
Aaron