You've got the basic procedure right, but there's a few steps that will trip you up unless you pay attention to details. The spider gear assembly and pivot shaft must be removed to gain access to the C-clips, by removing a locking bolt in the differential carrier. Slide the pin out, and remove the spider gears, including the thrust washers behind them. Push the axle shafts toward the center enough to remove the C-clips. It might be necessary to remove the brake drums to let the axle shafts slide in enough to free up the clips. Inspect the surface of the axle carefully. ANY roughness where the bearing rides makes it necessary to replace the axle, as the bearing runs directly on the surface of the axle shaft. An offset bearing is available to put the load on a different area of the shaft, but I've had less-than-great performance out of that fix. Pry the grease seal out of the axle housing, and use a slide hammer with a special expanding adapter to pull the old bearing. Some parts stores have a rental tool to do this, otherwise it's a real hassle to get the old bearing out of the housing. The new bearing will be a snug fit in the axle housing, usually needing to be gently tapped in with a hammer and a correctly-sized driver or a big socket to prevent damage to the new bearing rollers. Don't put any force on the rollers themselves, only the outer race. Install a new seal with the lip facing toward the inside, and lube it liberally with rear end oil. Put some lube in the new bearing while you're at it, to protect the bearing until oil can migrate down the axle tube from the rear end during normal driving. Be sure to clean any dirt or shavings out of the axle tube before installing the new bearing. I like to use a rag dampened with solvent, wrapped around a broom stick. Works great!
BTW, it's not necessary to dismantle the brakes. The axle will slide out of the center with the brake system intact.
Jerry