I would try a later bedtime... Maybe blackout curtains in her room for nap time too. (They definitely helped my DD around hat age!) Maybe she needs some teething tablets, a ring, or something for her mouth to feel better.
Also, letting her cry seems counter productive to me. When I cry, my head hurts, my face itches from the tears, my nose runs (along with whatever made me cry in the first place)... Not really the most sleep-inducing activity.
It seems to me like her body is changing again, and it is keeping her awake. I would say to give her some snuggles. Sit in a dark room, rock her, and when she tries to play encourage her to be calm. Though... If she doesn't want to sleep there is no forcing it. (Unfortunately. Lol.)
Of course, it is entirely possible that his is a short phase to struggle through, and she will start napping like a champ again in a few weeks. 12 months is a common age for another growth spurt, and lord knows babies' schedules get all jacked up during any new transition.
ETA: one other suggestion... Try changing the temperature of the room she is sleeping in. My DD sleeps better in a cool room, so I used to run a fan in there for her. (The white noise may have helped too...) My younger brother, at that age, (he is 5 now...) slept in a warmer room better, so we would use a space heater. Maybe something like that would help.
Also... If you are able to, maybe lay down in your bed with her and take a nap together. My DD usually sleeps longer (heck, the only time I can get her to nap at all any more...) if we are snuggled up together. Plus, you get a nap too! Win-win! (Screw the dishes... Lol.)