Last Chera Perumal who supposedly built this mosque ruled during the 12th century, that’s more than 500 years later than this imaginary date.
Scholarship disawoves it, the most radical date is Kugle and Margariti (2017) who date the emergence of the legend to 1540 - 1580, while the most conservative estimate from Prange (2018) places it between the 1100s and 1300s.
This is for the legend, the mosque itself has never properly had a date assigned by scholarly examination as far as I know, but it can’t have been too much older than the tale.