I am a freelance proofreader/copy editor. My clients are mainly people who are self-publishing their books - I format and design for them as well, so offer a package. It works for me as I've got a lot of contacts in that market and word of mouth has been an important part of getting out there.
The course you've linked looks suspiciously cheap for a proper proofreading certification. You want one either from the Chartered Institute of Editing and Proofreading itself (linked above) or one that is accredited by them (I did mine through College of Media and Publishing - a really good, comprehensive course that set me up well. It's a well thought of course in the industry though the CIEP ones are the best - and most expensive.)
You don't actually need a qualification, but if you want to do it seriously and look professional it will help - and if you're wanting to get into proofreading for publishers, journals etc you really do need some kind of background in it or at least show proven aptitude. I set up a webpage with testimonials from clients and that's a really good way of showcasing what you do and what people think - you still need a way of advertising that, though - I am a member of various writing groups as I am an author myself so it came organically for me.
I love it as a career - it suits me well because I write anyway and I've always been very picky about spelling and grammar. The course taught me a lot I didn't know - especially things to do with style guides - it's not all spotting typos, there's a whole lot more to it. It's a pretty intensive job and you need a whole load of patience - a lot of sitting at your computer. It can cause eye strain so you need to make time for breaks and other stuff. You need to be able to concentrate for long periods of time, and sometimes the material can be dull and dry as well as poorly written.
It's very satisfying to shape up a product - books, in my case - and to see clients happy with your work.
It's time consuming. I don't make a whole lot of money from it, but I don't at present charge very high prices as I'm still fairly new to it and am building my list of clients. I will be raising them soon, as I have to live - just be prepared to start small, to see how you get on, without really high expectations.