The gas port size is different for an 11.5" barrel than on a 16-incher. If you cut the barrel down to 11.5" (I would do this instead of 11"), you need the gas port enlarged to anywhere from .086" to .094" in diameter for proper function. There isn't a single gas port size to reference as it will depend on ammo selection to a large extent.
However, I would absolutely buy a factory 11.5" barrel rather than cut your 16" barrel. It will cost less to buy an new one and it will already be set up for proper function at 11.5" with a wide array of loads provided you buy from a reputible manufacturer. Similarly, you'll also be putting a lot of money into a used barrel when you could have a new barrel for less money and keep the 16" as a spare.
FYI- After you live with an SBR for awhile, you will discover reasons to shoot it with a Title I barrel, which is another reason to keep the 16" intact and in your possession. You draw lots of attention, which can be either fun or scary depending on your luck of the draw. Also some ranges will not allow the short barrel, even if legal. If an 11.5" is all you have, it's all you can do.