Do I need to report my stimulus check on my 2019 tax return ?

no. it is not taxable income.   on your 2020 return, there will be a calculation of the actual stimulus that you should have received. if it's your due more you get a credit (refundable). if you're overpaid you get to keep it without any tax consequences. 

Income you received in 2020 would not be reported on a 2019 income tax return, no matter what income it was.  And the stimulus check will not be taxable when you prepare your 2020 return next year, although you can expect there to be some questions about it when you prepare your 2020 return.