3D conversion of pictures for CNC carving

I am new to 3D and was wondering before I put a lot of time into learning the program if I Can use blender to easily take a picture of my dog and turn it into a 3D file (.stl) which I can then import into another program (Cut 3D) and use a CNC router to cut a bas relief in wood 3/4inch deep or deeper? I am trying to turn pictures of friends pets into 3D carvings and grey scaling does not work-- loses too much detail plus a dogs nose is black and becomes sunken while the nose comes out. If so is there any tutorial or someone I can contact to teach me? I have no CAD experience or really any experience converting photos. (Currently trying to learn photoshop but like I said grayscale doesn’t work.)