Interesting, in GMail I could download your keyboard layout file.
I have put it into a "keyboard layout collection", that means it’s in a .bundle file and can be assigned a language and an icon (I assigned Turkish QWERTY).
Then I installed it using Ukelele’s standard installation method, which uses the "Organiser":
You have to first set the folder where the layout file is located, so that you can see it and move it to one of the other columns.
Here, two versions are shown: the .keylayout file and the .bundle file (at the top in the left column):

After dragging the bundle file to the rightmost column, I logged off and back on. Then I could activate it in the usual way: