Precision may not be so high

according last response, accuracy is not good but can work for large areas. for this I recommend use NDVI with time series, however nothing beats going to the field itself and evaluate the crop

Try a combination of modis and Landsat, maybe a little better. MODIS LOW SPATIAL RESOLUTION and it depends on the size of the fields in the region you will analyze but  MODIS will not allow you to follow small fields (10 ha) check the area size of MODIS pixels . LANDSAT LOW TEMPORAL RESOLUTION (for what you want), Since LANDSAT .allows you to image the same region every 16 days with a 900 m2 per pixel, you can easily discrimante what fields were harvested but you won´t be able to know the exact day of harvest. So maybe a fusión of MODIS and LAndsat 8OLi would be a good approach for what you want.

You can use the  changing model of NDVI value following the cropping season from seedling to harvest, which determined from previous season. From the latest intepretation with the day of images acquisition, with growing stages determined, you can add number of days required until harvest, according to duration of cropping season, then the day of harvest determined.

MODIS at 250x250, since at least 6,25ha must be required

However the precision may not high as previous answers and comments. You should

combine with other high resolution images as landsat, Spot, etc