Most firms prob. don’t care what your degree’s in. They’re just happy you know how to read. But, if you do decide to take the 2 year program, just go an extra year and get the law degree. It’s a lot more cost efficient.
Does QA Test Engineer mean you’ve been working in a technology company? You might want to look into becoming a patent paralegal (e.g., a docket clerk or foreign filing administrator). They get paid significantly better than other paralegals, because of scarcity. You might have trouble breaking into the business with no training, though - I don’t know exactly how you’d go about it. Don’t bother with the certificate if you decide to go this route - you would never do one thing that you learn during the program.
Thinking aloud here - maybe you should look for a firm with a smallish patent department with overworked paralegals, and see if they’d hire you as a general assistant. Then learn the ropes on the job, and either convince them to promote you or go to another firm.