Then you're using a longer lens or you have a larger crop factor than you think. The full moon is 0.5° (approximately ... it goes from around 27' to 32' but 0.5° is a good approximation). If you're using a 300 mm lens with a 1.5x crop factor, that's the equivalent of 450 mm. A 450 mm lens gives you a field of view of around 4.6° ... 9 full moons' worth.
I have a 1000mm lens. I have a 1.6x crop factor body. When I put my camera onto my 1000mm lens, the moon usually just fills the vertical field, but usually there's still around a 10% buffer.
I just did a quick search and it looks like most 8" Dobsonians have a focal length of 1200mm, though when doing eyepiece projection, as the original poster did, the rules about how much of the field of view the object fills up no longer apply as easily.
So in general, using a telescope gives you a longer focal length and a larger aperture (the larger aperture being the most important factor usually). In the original poster's case, it's her only option as opposed to a long lens because she's using a P&S.