I have some 20 lady watches with this small lady movements, but only one has a date feature. So I think it is a rare watch.
In the middle is a rare Twin Fish (shuangyu) lady watch made by Dalian Watch Factory, and on the right is a Rose(Meigui) brand made by Nanning Watch Factory. These two are also uncommon brands. Dalian also made a Zhenzhu (pearl) brand lady watch that is more often seen.