That lens has one review, 3 out of 5 stars. What should that tell you? I will tell you. The lens requires a robust tripod, with a robust head for best results. Remember, it is not a fast lens, so it will also require well lit subjects. The full moon is more than well lit.
I had a lens, Vivitar 650-1300mm f/8 that was very similar to that lens, and passed it along to one of my sons The image quality is comparable to the Series 1 Vivitar 75-210mm F2.8-4.0 lens that I bought in the 1980s. The lens had great image quality in its' day, but it is mediocre today.
The body construction of the two lenses are similar. The lens has a zoom locking ring that twists, which affects the horizontal orientation of your camera. You wil find yourself using two hands to tighten the zoom locking ring: one hand to turn the ring while the other holds your camera level.
Since it is a fully manual lens, you will be forced use a tripod, not unless you have four LONG arms, two to zoom and two to focus. You will find yourself using the rear LCD screen to focus in LiveView mode. However, because of the long focal length, you find that the tripod foot transmits vibrations and resonances, which will make focusing difficult. The image on the LCD screen will jump around as if you were witnessing an earthquake, which is why you will need a VERY robust tripod/head setup.
You will capture better images of the moon using the 70-300mm kit lens and cropping them. Using the Vivitar doubler will only magnify the chromatic distortion of any lens that you use it on, as well introducing some of its' own. If you are shooting the moon, then you will not notice the vignetting from either the 500mm lens or the doubler.
However, the Vivitar 500mm lens is a good tool to learn on. It is just simply not a keeper. The lighthouse looks pretty good until you zoom in on it, where you can see the purple fringing of chromatic distortion.
