Given that Prim is the first character to bring a farm animal aboard the Enterprise, there are no IC arrangements at this time. Since Lady meets the standard size requirements for a pet, she can stay in Prim's quarters. If, however, you would prefer she not stay in Prim's quarters, IC arrangements will have to be made to find a suitable cargo hold and convert it into a permanent living space for Lady. Since there is no canon evidence that there are other long-term or permanent farm animals on the ship, Lady will be the only animal in this area until/unless someone else apps a character with an animal needing the same arrangements.

The conversion of a cargo hold into a suitable stable can be largely handwaved, after OOC deciding on the basic features of the room. Thus, if you decide you would like to stable Lady, that can be arranged with little to no waiting or IC threading once OOC arrangements have been made.