LesTyebe: Confirmed. Adding the -enabledeveloperconsole to the text line in the Target box in "Properties"(right click shortcut) works, but only with the shortcut found in the bin_ship folder. The shortcut which works for me is the one with the blue Grey Warden griffon symbol on a golden kite shield, not the red dragon icon. For some reason, the red dragon icon shortcut is the one placed on the desktop during installation so at first I assumed it would work to add the extra text to the target box in "Properties" of the red dragon icon shortcut, but it only works with the blue griffon shield icon shortcut. At least that is how it worked with my machine.
ErisYumi: I just wanted to say this is what worked for me. I tried to do it via the shortcut GOG creates for you and places on your desktop but it wasn't working. Doing it with the launcher found in the bin_ship folder did the trick for me.
If you're using the Galaxy client to launch your game, another option is to add a custom executable to the DAO launch page:
1. Click the Settings button (next to Play) and select Manage Installation > Configure.
2. For Launch parameters, select Custom executables / arguments.
3. Under the File 1/ Default executable section, click Duplicate. This adds a new section (File 4).
4. For File 4, use the drop-down to select "Select executable". Browse to select the DAOrigins.exe file (located in ...\Dragon Age Origins\bin_ship).
5. In the Arguments text box, enter -enabledeveloperconsole
6. Add a custom label. If you want, you can make this the default executable too, but I only use it when I need it.
7. Click OK.
8. When you want to launch the game with the developer console enabled, don't select Play. Instead, click the Settings button, and select Additional executables > YourExeLabel.
NOTE: You do still have to install the Make Console Commands Visible mod from NexusMods to see the commands as you're typing them (basically it's just adding a font file). Don't worry about changing key bindings if you're using a US keyboard.