Telstra has a modem testing system, called the Modem Online Diagnostic System which you can use to exercise and provide diagnostic information about your modem and your telephone line.
Access to the service is via the 1100 Service Difficulties and Faults number. Describe your difficulties or problems with your modem and you will be passed onto a technician who will look up your 'phone line records and who can register you with their testing service. This registration basically gives you a login which you use to access the testing system. The test is run by you by simply dialing up the 1-800 number that the technician gives you and entering your telephone number. Their system then exercises your modem and the telephone line automatically for a predetermined time and then sends you the results.
The results are also kept on their system and you can discuss these with the technician at any time. Registration lasts for two weeks typically.
Following are some snapshots of the results obtained using two different modems on my telephone line at home.
Here you can see the factory defaults being loaded and the Telstra number dialed. The modem-to-computer speed was 19200.
Other tests (not shown) indicated that it is only at 28800 baud that this modem exhibited this problem. At 14400 baud both error detection/correction and compression could be enabled with no resends.