Yes 10Q can be rooted. Once the windows "ADB Interface" driver is installed. I did have problems locating the 64 bit driver for Win7, so I used WinXP 32bit with "Super One Click v1.5.5" to root the phone. Once rooted I was able to flash the EVE with LG's Firmware Update program. Flashing with V10Q_00.kdz did not correct the unstable system UID's.
So I tried a V10T_00.kdz flash from a LG KH5200 this was successful and corrected the system UID problem. Although the phone info said it was a KH5200 it worked. I was also able to enter the hidden menu by typing 3845#*5200# and enable root permission, see below. I also had to change the keyboard setting to get correct symbols by deselecting "LG IME" in the keyboard settings.
1. Enter this on the handset to get to the hidden menu: 3845#*620# (3845#*5200# on Korean firmware)
2. Select: Module Test -> Stability Test -> Enable Root Permission
3. Newer roms require a password: EVE&ADAM&&620LOVE!