Ideas from other Hometalkers
You can you tube on how to make a cabinet and adapt it to your size. I would use a small chest or furniture cabinet and adapt it for a vanity. I've done that several times for clients andvitvworks out well. Add a marble or granite top for durability. Be creative and think outside the box. Repurposed furniture is fun
Here is a step by step tutorial to help you with this project. https://www.instructables.com/id/DIY-Rustic-Bathroom-Vanities-How-to-Build-Woodwork/
I like this one.
If you do not already have all the requisite tools for wood working, including a table saw, that you will need to construct a vanity cabinet, it may be more cost effective to purchase a ready made one. Or, as Kelly suggested, diy one with repurposed furniture.
Here are some examples of items that have been 'up cycled' or repurposed into unusual bathroom vanities.
Here’s how we built a floating vanity: https://www.frugalfamilytimes.com/2017/11/how-to-build-modern-wood-floating.html?m=1
if you have a piece of furniture that you would like to use (look at thrift stores) you could build one from that and then paint or stain the furniture piece - here are more ideas