Well, my one is from a Japanese company "Logitec" (different from the American Logitech, which has to be called "Logicool" here because Logitec was here first). Here it is: http://www.logitec.co.jp/products/bluetooth/lbtuan04c2bk/
But as far as I can tell, it's a completely bog-standard rebranding of the CSR8510 A10, which I think is available everywhere under various brands. If you go and get a miniature Bluetooth 4.0-USB adapter from your local store, it may very well be exactly the same thing in different packaging.
Here's another product based on the same chip: http://www.lairdtech.com/products/bt820
Now, CSR's product supports HID Proxy mode, but most (all?) vendors don't enable that by default. Enabling this feature is done by setting the "pskeys" (Persistent Storage keys) on the chip. Using Linux, you can do this using "bccmd" which is built into the bluez Bluetooth stack. My understanding is that you can do that on Windows too, but you need to use some software that CSR wrote and is proprietary.
If you use bccmd to set the PSKEY_INITIAL_BOOTMODE key to 0x0002, then unplug and replug the dongle, it will come up in HID Proxy mode.
In HID proxy mode, the computer sees it as a mouse and keyboard. Confirmed in Linux and in OS X (OS X actually pops up an assistant to kelp me configure my new keyboard). However, these apparently only work with Bluetooth LE devices, which I don't have any of, and which is where I'm stuck now.
Documentation is very very scarce (the datasheet for the module seems to be a well-guarded secret), but I found this from a technician in CSR's forums:
"CSR8510-A10 in HID proxy mode supports two HID-over-GATT connections. PSKEY_USR16~23 describe the first connection and PSKEY_USR24~31 describe the second connection. It does not really matter what type of device is being used for the HID-over-GATT connection (mouse, keyboard, remote control, digitiser etc.) [...] So, PSKEY_USR16~23 should contain HID descriptor from the device's GATT database (that cover both keyboard and mouse)."
So, what I need to do now is figure out what "HID descriptor from the devices' GATT database" means in the case of a keyboard, and store that data into PSKEY_USR16 and up. But for now I'm stuck until I get my hands on an actual BLE keyboard. Maybe the Windows device drivers for the dongle will write the correct data into PSKEY_USR16-23 when it's paired; then I can look at them and see what's in there.