typically the monitor will report its capabilities to the graphics driver by submitting its EDID. This one contains the modes that are supported by the monitor. If the monitor really supports 1920x1080 it should be listed as resolution in the Catalyst Control Center->Desktop properties. If not you might want to double check how the monitor is connected e.g. if you use miniDP to DVI dongles that are supported. A list of qualified dongles can be found on: AMD Eyefinity Technology - Recommended Adapters
If for some reason you want to add a resolution which is not listed you can add so called custom resolutions. I would recommend using the CVT-Reduced Blanking Timing standard. The you just need to enter the required resolution and refresh rate to get the mode added.
Please note that if you want to create Eyefinity Display Groups those custom resolution will not be taken into account.