A good way to test these sorts of GET queries is actually just doing it in the browser - makes it very easy to confirm behaviour. That said to get what you're looking for you just need to do a GET to the following:
https://<MyKey>:<MyPassword>@<MyShop>.myshopify.com/admin/orders.json?fulfillment_status=unfulfilled
fulfillment_status has some special filters you can use to return what you want:
fulfilled -> Orders that have been compeltely fulfilled
unfulfilled -> Orders that are unfulfilled or partially fulfilled
partial -> Orders with partial fulfillment
restocked -> Orders that have been restocked
shipped -> Orders that are completely shipped
unshipped -> Orders without any fulfillments
Importantly, null doesn't behave the way you're expecting. For one reason or another (I'm going to have to look into this) the json endpoint returns all orders when searching for null. Using the filters above should work, though