If all you need is a basic one-page website with an email address, phone number and maybe your business address, you can absolutely do that yourself. There are many website builders and one-page templates you can use to get up and running quickly.
Creating an effective website is hard work - at the very least it involves design and SEO know-how – and for this reason self-builds are incredibly inefficient. Instead of exerting all your energy building a website, your time is much better spent doing what you do best – running your business.
Domain registration doesn't need to be pricey. Registration services, such as Dot TK and Freenom, offer free domain names, and they'll get the job done provided that you don't mind a funky-looking URL extension.