Some people seem confused by this, so I thought a guide would be appropriate.
You need to get to the Quest where the Quest Master actually tells you to put the Dove in for you to do the Quest. You should get to this point fairly quickly, in one or two days.
Go to the left of the screen and click 'Profile'.
Look for a link that says 'Edit Profile' (it's below your name) and click that.
Look at the 'Medals' section on the bottom. It should look something like this:
Category Rank Week BB-Code
Beginner's protection [#0]
Now type that code into your profile. This is where it's easy to mess up. Remember to put in the brackets, and use a zero instead of an O. If you can't type brackets, copy-paste the code. It's right here. --> [#0]
After putting it in, go to the bottom and click 'Save'. Your quest is done! Check with the Quest Master.
Should you ever want to get rid of the dove, you can take it back out by going back into your profile and deleting the code, after you finish the quest that requires it. The dove itself doesn't give you any protection, it is only for the quest and for display.
Addendum: A new guide with pictures has been posted, by DTD.