i have tried the emulator with my set up (see signature) and it ran the games i had well enough at high resolution's, some games do have issues but that is expected with an emulator, but one of the best emulators i have used in a while since PCSX2.
im guessing bet results are with an actuall wiimote with sensor bar, haha, was using a xbox controller for most of it and have to keymap the motion of tilting and shaking to buttons which is very hard to do while playing something like new super mario bros.
Your computer will handle Dolphin fine at 1080p resolution, the issues you'll run into will by and large be overcome by tweaking the settings in the Dolphin emulator. You will definitely need to OC your CPU however, just a heads up. Look for about 4.5ghz+