6 quarts should be plenty of oil for the rear axle. If you need to get more, well that is another trip to the store.
I bought a small pump that goes into my drill to move the oil out of and then new oil into my rear axle. It really helps, as there is not a place to pour in the oil with a funnel on the F-350 that I was working under.
I guess you already know to fill it until it starts weeping out of the filler hole? The oil lubricates the outer bearings, so there will be some in that tube all the time. The vehicle needs to be level, so if tilted toward the passenger side, you might end up with a lot of fluid in that side, instead of in the rear axle housing. .
Fred.