I like the idea, however, I think it may become very limited and there will be only so much you can do with the duck for dress up.
Also ... eg.. Google, when you sign in, your settings are there, even if you delete your cookies, etc... I think if someone dresses their duck, cleans history and such, they will lose everything they do which in turn may not be so appealing.
If you could sign into DDG search and keep settings, that may make the dress up idea better. If it was a full duck, not just the head, I would think it to be even better but just being the head, in my opinion, it's better to keep simple color changing.
But of course if you do decide otherwise, just ask, I'll help.