How can I make over a plastic laminated wood dresser?

You can paint laminate - there are several posts here on hometalk which should help you https://www.hometalk.com/search/posts?filter=paint%20laminate%20cabinets

Chalk paint would be your easiest option. No prep work and a nice modern finish.

I have also used crackle coat on laminates. First your base color latex, crackle coat, and then your top color. I like a medium brown underneath