It looks like an 18" vanity, the kind with legs.
perhaps even turned sideways?

Cool pic.

Well the towel is hiding the style but judging from the cab next to it is is just a simple white shaker cabinet with either a white laminate or a white painted wooden top.

Once you have your sink size then just get a shaker style sink cabinet and put a white top on it. It's a simple style that any cabinet manufacturer would have. You might even be able to pick one off the shelf at a big box store depending on the size.

They trimmed it out with the interesting towel bar but basically a box is a box.

I thin CEF is correct. That appears to be a curtain--probably no doors, similar to this:

Here is a link that might be useful: google search 'wash stand' scroll down