Welcome!
We got planning in the greenbelt (eventually) by starting a pig farm but needed a business plan that would give us an all year round income, so diversified in to chickens (meat & eggs), turkeys, ducks (meat & eggs), fruit and veg and sheep too. Once we proved we were serious about developing and running a viable, profitable business (not on paper but in practice) our other argument was the security of our animals and equipment as a NEED to be living on site. Our business has now grown so large that it has delayed the building of our house!!!
Have a long think if this is the kind of 'battle' you want to get in to....it has taken over our lives and although we wouldn't now change a thing, had we known how big a venture we would have to develop and the length of time it would take to achieve planning we might have thought twice about starting in the first place.
The planners have seen and heard every argument for permission and will want to see plans put in to action to show how serious you are. There are no easy options and I would be very sceptical about planners allowing a house based on a couple of alpacas.
Best of luck