There are a few options to do this:
1) Export CDR/CMR from within CAR, can specify a from/to date:
http://www.cisco.com/en/US/partner/docs/voice_ip_comm/cucm/service/6_1_1/car/carexprt.html
2) Configure a billing server to export raw CDR/CMR files, would only export files generated after configuration, not terribly useful for your scenario, but might be useful moving forward:
http://www.cisco.com/en/US/partner/docs/voice_ip_comm/cucm/service/6_1_1/admin/sacdrm.html
3) Generate an AXL/SOAP call to get the CDR files via CDR On Demand:
http://www.cisco.com/en/US/partner/docs/voice_ip_comm/cucm/devguide/6_0_1/ccmdvCh2.html#wp72438
Unfortunately, the report generation search reports are a bit limited. You can query the car tables via the CLI, but that is probably less user friendly than pulling the data via export using #1 or #3 above.
HTH!
-jt