You request an extension for your 1040, not for the supporting documentation. Note that the extension applies to your filing only, not to your payment. Anything you owe is still due not later than April 15 or postmarked by that date In essence, you still have to figure everything out by the 15th. If you don't have the 1099 and don't know what it will show, make your best guess and figure things out on that basis so you can pay that by the 15th.
If you know for certain that you will be due a refund, of course, no payment will be due, but you have to request an extension anyway -- that doesn't become any less important.
