Her sleeping time sounds right-on for her age. My daughter is restless and cries out in her sleep, too. Unfortunately, I don't think there's a solution for that.
How long has the night-waking been going on? My daughter (now 2yrs) does this in spurts. Usually we could link it to a physical cause, such as teething, growing pains, sinus problems, reflux, hunger, or gas. But for a few weeks it seemed to be just psychological. Crying it out never worked for us either; going to her each time she cried made her feel more secure, and - I think - made the spurt end faster.
Something we've always used (because my daughter is a light sleeper) is white noise. We use a HEPA filter, which also cleans the air and maintains a constant whirring sound. A table top fan or white noise machine works, too. It helps drown out noises that can wake her up.
Take her to bed with you only as a last resort - babies like to make that a habit very quickly. I've read that these trials do eventually end, so hang in there, and sleep when she sleeps. Laundry and dishes can wait. Chronic sleep deprivation definitely has a physical effect on the body, similar to chronic stress. So take care of yourself, even if that means letting some household chores wait while you rest.
Best wishes!