INVOICE DATE

The date of an invoice is only useful as a point of reference. Usually the date assigned is the date it was prepared or sent. 

I think it is more helpful to your bookkeeping to date invoices with the last day of the period that it covers. That approach puts your time expense and the associated income in the same timeframe.  
​
The date is now meaningful and it may spur your client to make payment just a little sooner.