Good start Ian!
Does your camera have exposure controls or shutter speed controls?
As silly as it sounds, when I used my
first digital camera (kodak 2mp point and click - no manual controls), if I turned the flash off (as you think you should), the camera would over-expose the dark image trying to get exposure right, and so the moon was always very washed out (like your image).
I found that turning the flash on tricked the camera into not overexposing the image, so the details came out much better. You could try this, and tape something over the flash so you don't blind yourself
If your camera allows you do manual adjustments of exposure or shutter speed, then use that instead of the flash.
This is my very first (that worked out) afocal moon shot using my old Kodak 2mp, using a 25mm or 32mm eyepiece (I can't remember).