It depends on either your period is still open or closed. Let's say, you are in July of 2019 but have just recently received a bill from December 25th of prior year. If your books are closed, QB will not let you enter unless you force it, which is not a good idea anyway. Most likely you would have already closed your books and filed taxes by now. And if you do decide to force-enter old invoices in QuickBooks in prior period, you would not benefit from the reduction in taxable income when you are filing taxes next year, not to mention the fact that your books will not match your tax records.
So, to sum it up, if you have to enter invoices for a closed period, post date on the 1st of current period. However, if the period is still open, proceed as usual, entering the actual date.