What kind of DSLR takes photos like this?

As in, like with that kind of detail, especially around the eyes.

Could I get it with a Nikon D3100?

Thanks.

Added (1). Could it also take photos like this?

I want it to do that thing where the eyes stand out heaps, it's almost surreal.

Any dSLR has the ability to do that. It's up to the photographer to choose the correct settings for those kind of shots.

Absolutely! The D3100 is a great choice. However its not just the camera that causes pictures like this to happen. Knowledge of lighting and a bit of post processing will do loads of favor. Notice how it wasn't shot under bright sunlight but softer even light…

Also a better lens than the kit lens is the 50mm f/1.8