I’m a DIY kinda girl so the limitless possibilities with infusing anything completely appeals to my Gemini nature (I like loads of options). This flavor profile sprang to mind as I see a similarity to the intensity of the flavor of juniper berries and felt it would stand up to the venison.
Because rosemary is a strong tasting herb this should be plenty of time to develop the flavor though if you want an even stronger flavor leave it longer. When it has reached the flavor you prefer, remove and discard the rosemary (which will have turned brown and colored the gin slightly). If you want to make a larger batch just add additional sprigs of rosemary to the volume of gin.