Yep, they don't need much head room at all, a foot and a half is perfect. They'd love being out on the grass
You could get a little house like this for the run
http://www.zooplus.co.uk/shop/rodents/cages/rabbit_hutches/natura/33223
or something similar. I really think they need a little house in case they get cold or it rains, or is too sunny, or if they just get scared and want to hide.
Make sure the run is safe though, from cats or even foxes or dogs that might be around, and has a lid. Also that there are no spaces under it, because they can get through tiny spaces. I almost lost one of the baby pigs when there was a little gap in one corner, where the run wasn't pushed into the grass properly. He was wandering around the patio with all my cats around!