we had a dog attack here a couple of weeks ago, lost 3 ducks, had 4 more mauled (but recovering) and 2 chickens and a turkey went missing. I did a thorough search for them the afternoon it happened and again the next morning without success. took 3 days, but the missing birds did come home. might try doing your usual chicken-feeding call a couple of times a day for the next several days, hopefully she hasn't gotten too far and that will help her find her way back.
it is a risk with free-range birds, we lose one occasionally to hawks, part of the free-range deal. still, 2x on being armed and protecting your livestock. it's a shame for the dog, but you can't have them killing your animals. stupid owners... they're the ones that should be picking bird shot out of their rumps.
if the dog's on your property as a frequent activity and you're not wanting to kill it outright unless it is on your birds, I'd get a bb gun. they're a useful educational tool. if the dog's in your chickens already, a shotgun won't help, you could end up killing birds along with the dog.
and of course, if you're going to arm yourself, get to the range and tune up your skills. You want to know where those bullets are going, even if it's just a .22 ... you'd be surprised how much your aim is affected by the stress of the moment.
hope your bird makes it home.
oh, one more thing, you do need to know the local, county and state regulations regarding defense of livestock and discharge of firearms. where I live now in MO, it's not an issue, but in CA where we used to live, it is. we spend a LOT of money on legal defense over defending our livestock in what appears to be a rural area, but is barely inside city limits. had a visit from the SWAT team too. BAD situation caused by stupid CA laws and firearms paranoia, along with a paranoid neighbor. before you get into that, you will want to know the applicable laws. just one of many reasons we no longer live in CA. and love living in MO.