Yes that's the right model for standard (non thick) 5.13 gears but it won't work for yours. Assuming your present 5.13 gears are installed onto the factory Rubicon locker, those same gears cannot be moved over to that particular model of Detroit Locker.
The issue is your Rubicon Locker is made to hold 3.73 and down. When you want to install 4.10, 5.13, etc. you have to buy special 'thick' R&P gear sets which would not fit the above version of the Detroit Locker.
What you can do is get the other version of Detroit Locker which is made for 3.73 and down and you can then bolt your existing ring gear to the new Detroit. Set the back lash and you're good to go. Like this one that will accept your current ring gear since it has the same ring gear position as your current Rubicon locker.
https://www.justdifferentials.com/Dana-Model-44-Detroit-Locker-p/det187sl-16d.htm