My new place has a lot of rabbit bush. The grass was over grazed on much of it Drought has really encouraged the rabbit weed in the severely over grazed areas. What is the best way to deal with it as have not heard it's an edible weed? Can use alternative livestock without a problem. Place is about a section and a half and this is a one woman operation. Am implementing a grazing plan after getting some tests run/results back by the folks at the NMSU Corona Research Ranch. Won't be running cattle until this fall (fence to update) and those will be Devons from the Bar 10 in N AZ/S UT.
Nature is a wonderful teacher. Just when you think you have things figured out, she'll show you how wrong you are...keep trying, you will get it.
I'm not familiar with Rabbit Bush so I will answer only in a very general way - and I am assuming that you are ranching in New Mexico, dryland -extensive rangeland conditions.
getting your pasture rotation implemented, especially if you can use daily pasture moves, is a fantastic way to create the kind of conditions that allows grass to begin to flourish again. Whether the cattle actually eat the scrub brush or not is not actually important - as they come through they will trample and crush and scratch and maul all these other plants that you don't want, before your herd moves along. You won't see miracles happen in a single grazing rotation, or even in a single year or two, but repeat, repeat, repeat with iron-discipline using DAILY pasture moves to keep the cattle impact brief on each pass, and you will see the land begin to shift back to grass.
Furthermore, coming back to the principle of using your cattle as your primary land-management tool, a well-planned electric fencing system, like the Smart Electric Fence Grid series described on my Electric Fencing page, puts a powerful tool at your disposal to shape the land according to your goals. One day you may bunch your animals over bad sections (or toss out a bit of hay to create some rodeo-like commotion) so they trample the daylights out of some of these scrubby areas, and the next day you may be very gently grazing across sensitive new growth, or skipping a section of pasture altogether, if that's what it needs to help promote recovery.. It takes patience and a skillful hand, but directing your cattle impact through your herd impact is the way ahead. That's how you can slowly "bulldoze" these bushes out of existence with your cattle herd while gently encouraging your grasses to take root.
Focus your time and energy on setting up your electric fencing and water grid and learn the art of DAILY pasture rotation (especially important in your dry climate) - your pasture rotation will be your most powerful tool in rejuvenating this land. And make sure you take lots of photos - before, after, and along the way! And please share your journey as it evolves - I've recently set up a location on my website specifically for farmers to share their experiences to provide success stories to motivate others (and ask questions along the way!).