Can I take pictures like these with my setup?

I received a Nikon D60 with an 18-55mm lens as a gift. Do I need anything else to make shots like these?

My girlfriend likes to model and I think it would be nice if I could photograph her sometime for fun.

A tripod and flash will help the best thing you can do is read the Manuel that came with camera and practice you will not be able to get shots like those straight away

Yes, you need some off camera lighting - all of those were likely taken with an off camera light source.

As well as gear, you need the knowlege & experience to light properly.

The first shot was done using indirect natural lighting.
The second was shot exposing for the background and using flash fill
The third is similar to the first, indirect lighting probably using natural lighting too.

You have a older dSLR, so one might expect you have had time to learn how to use your camera and see light and have some kind of idea how to emulate just about any lighting you see.