If it's only one exposure, it's not an HDR. You can mess with the contrast, black levels and saturation to get the same 'look' as an HDR. Same idea as using an HDR filter on your iPhone... but really that's all it is. A filter.
I would give it a shot on your D3100 BadMoon. Granted it would be easier if you had exposure bracketing, but it's still doable. A tripod and a remote shutter release are essential though.
You do not NEED autobracket to take HDR's - it just makes it easier & means less fiddling about. Here is how to take HDR pics without AEB;
1. Put camera on tripod.
2. Turn off Auto ISO (if you have it on, it may be on by default).
3. Set mode to aperture priority (A). Set aperture to get a decent depth of field - f16 or so.
4. Take a shot - this will be your 'normal' exposure, ie 0EV
5. Dial in a stop under exposed - use the +/- EV button/wheel until it says -1.0EV.
6. Take the shot.
7. Repeat taking images by adjusting the +/- EV comp wheel until you have a series like -2EV, -1EV, 0EV, +1EV, +2EV.
I'm far from an expert though... Just messing around and exploring.