I cannot tell much by that pic. If you will show the pinion flange side and the other side of the ring gear carrier, I might be able to tell you something. It looks to be a generic 9" . If you want to know the gear ratio count the little gear teeth and divide into the big gear teeth.
U joint cups are usually 1 1/8th inch, with some 1 inch. If the pinion and carrier bearings feel good, you are probably in good shape. Do not remove the pinion flange, unless you are familiar with the crush sleeve and bearing pre load. If this carrier leaks it might be on the pinion seal. With no signs of leaks, leave it alone.