I agree with Robo; a small revolver or semi-auto in .380 or .38 spcl. would be a much better choice, to say nothing of the potential liability issues for using a single action pistol (the exact same that would be brought up in a Civil matter if you used a single action revolver.)
That said, however, a derringer is much better than nothing. I would suggest an American Derringer, Model 1 or 3, in a large caliber - .45 LC at a minimum. Bad guys do not like to see a big hole(s) pointed at them, and are more likely to run than with a small hole pointed at them.
As a primary self defense gun, not a good idea. Limited to 2 shots in most cases, clumsy to reload, not accurate, larger calibers have very hard recoil, limited range and poor performance because they dump thier energy out of the short barrels. Good advise from robocop and deerhuntguy.
Having said all that, I have always owned a derringer, and sometimes carry one as a back-up. They can be fun to shoot and are better than nothing, but never as a primary firearm. Get a good light weight, hammerless .38 cal. snubby.
Sure we'd all rather carry a Mossberg 590 when the crap hits the fan; but I wouldn't feel naked with a derringer in my pocket.
Most derringers are available in calibers that will outperform the .25ACP and the .32 ACP that I carried when the weather or my dress didn't permit anything larger. Is a 6 shot .25 really better than 2 shot .44 special?
Nah, practice with your derringer, find it's limits and yours, and be happy with your choice.