Like Nost said....make sure they are not back to back....
The outside outlet 'should' be attached to a stud.
Since you are cutting a new hole inside the garage, you will be using an 'old construction' box. This is the type that has tabs that pop up into place to hold the box. Hence, you really don't need to install it next to a stud....you can, but not necessary.
Figure out where that stud is that the existing outside box is attached to...that will give an idea of the area you can put your new box. Looking at the photo, I would assume your new box is going to be higher than the one outside.
Determine your spot...cut the hole to match the box.
Outside...remove the outlet...knock out a hole in the top of the box and fish your wire up to the hole where the new box is going to be.
Be aware, you might have insulation to deal with....
This is one of those jobs that is not hard....just tedious....
Also be aware that your outside outlet is (should) be on a GFI....which is ok...because garage outlets are also supposed to be on a GFI. I doubt load is going to be a big issue in that it's unlikely you would be using both at the same time.