you really do not need a gasket for the differential itself, black RTV works just fine. I have found when people use gaskets they usually split them by tightening down the nuts too much thus causing a leak. factory never used gaskets for the rear diff.
now, with that being said.. getting to your axles. they can be pulled out without removing all of your rear brake hardware, just be weary of the lever between the two brake shoes... you can lift it up a smidge to pull your axle out.
I would pull your axles all the way out so they do not rest on your inner axle seal. this weight can cause a split in the seal thus causing a leak. speaking of which, it is a great time to inspect that seal while the axle is out to determine if it needs replacing. if it is the OE seal, then replace it.
step by step:
1. loosen lug nuts
2. jack up rear end of car and place on jack stands
3. remove rear wheels
4. remove brake drums
5. remove the 5 nuts that hold the axle flange
6. lift up brake drum lever that resides between the two brake shoes, and pull the axle from the axle housing ensuring that you do not put any pressure on the inner seal
7. inspect inner seal for premature wear, remove and replace if it is the OEM seal
8. remove driveshaft
9. loosen and remove each nut on the differential carrier
10. place a drip pan underneath the differential carrier
11. use a screwdriver and a hammer and pry the bottom of the carrier away from the housing to drain any and all fluid
12. once fluid has been drained, remove pan and use a floor jack with a board and place under the carrier and pry carrier away from housing so that it will be supported by the floor jack
13. clean out any old fluid in the axle housing with papertowels
14. with a razor blade or your preferred method, begin to remove any old silicone in between the studs on the differential, ensuring surface area is clean of any contaminates
15. apply a decent coat black RTV in between and around studs (attempting to veer away from getting to close to differential opening on housing)
16. install new differential carrier using your manly muscles or a floorjack
17. replace all differential nuts to studs and tighten in a star/opposite pattern (I use nylon thread lock nuts)
18. replace axle's in reverse steps as above
19. let silicone set for a minimum of 12 hours prior installing fluid
20. 12 hours later add your gear oil through your brake vent bolt hole or on the side of the carrier (seen it done both ways).
21. start up car and put in gear and let wheels turn to get fluid flowing throughout the entire housing before putting a load on it.
22. let car off of jackstands and start driving it