That will certainly do the trick.
Whilst the job isn't difficult, unless you have the right parts to adjust the gear backlash it can be difficult to get it right.
But basically, drain the oil (and whilst that drains) pull off the both wheels, brake calipers and rotors, remove the 4 bolts for the axle retainers and pull each axle out about 150mm ( reverse the rotors onto the axles, put a couple wheel nuts on a few turns and use the rotor like a slide hammer. They don't have to come all the way out). Drop the panhard rod and remove the rear diff cover.
Use a dial indicator to measure the current gear backlash. Undo the 4 bolts holding the bearing caps in place. Use a pinch bar behind the centre (against the pinion) to lever the centre out. Make sure you keep the bearing caps and shims together on the correct sides (this is critical).
Swap the old bearings and crown wheel onto the new diff centre or you can use new bearings and then re-assemble the diff centre into the housing (making sure those shims go back in their original positions), button it all up and then measure the backlash. IF it's the same as before then go buy a lotto ticket, re-assemble everything, fill with oil and you are on your way.
If the backlash is different then it needs adjustment, if it's only a touch off it may well be fine or the gears might be a bit noisy when driving. If it's too tight, when things heat up there may end up been no backlash which will cause damage. A little looser not such an issue but again might cause gear noise.
The other option is to take it to a shop to fit, they will try and convince you to replace all the bearings and seals whilst they are there and lighten your wallet a bit more. With the axles, there is always a chance the seals might leak on the end of the axles (but this the fun part of playing with cars).
