TR - Since you just purchased your car,I would definitely change the diff fluid. Here is how I change mine. I will drive the car breifly to warm up the diff oil so it flows better. I raise the rear of the car and remove the spare tire carrier. Remove the plug on the back of the diff housing,it's on the passenger side of the housing pointing back,If I remeber correctly just use the end of a 3/8" socket extension. Then,using a suction gun(refer to picture), suck out the old oil. You will need 3 bottles of GM# 1052271 and 1 additive GM# 1052358. Using the suction gun,suck the oil out of the bottles one at time and shoot the oil into the rear until it reach's the top of the fill hole. You will use almost the entire amount of oil. I always put the small bottle of additive in first,followed by the 3 larger bottles. Put your spare tire carrier back on and away you go. I change mine every 2 years.
You can purchase a suction gun at any auto parts store for about 10-15 bucks.
Dave
edit: after checking my records,You will use a small portion of the 3rd bottle not the entire amount.