Good news and bad news,
The good - I've been asked this question at almost every outage. The bad - there is no simple answer. Most get into QC by being a craft worker at a major plant and getting a job change into QC. QC and QA are different jobs and need different skills, QC is looking at things and work; it's inspection and observation. QA is looking at programs and processes, following the paper trail. Often QA comes from college engineering, operations or security supervisors who don't want to supervise anymore, a sideways shuffle from procurement engineering, or from some other field such as aerospace or manufacturing.
The American Society of Quality (ASQ) has some classes, given what you said was your background, the most relevant one is for Mechanical Inspector. Google ASQ for your local region and chapter, they have web pages that will give you info about dates/places/costs.
There are also requirements about experience and education; more college, less experience, of course. Nuclear power plants are not driven by a Nuclear Reaction, instead they are driven by Nuclear Regulatory Guides, from the NRC. These can be found on the NRC web site. Reg Guide 1.8. It says that Supplement 2S-1 of ANSI/ASME NQA-1-1983 should be used for qualification criteria. But if you are a welding inspector there is another standard, ASNT SNT-TC-1A. (Yeah, welcome to the Nuc world buddy, paper and regs and standards). But the basic level (QC Level 1) requires 2 years of experience in equivalent inspection, exam, or testing, or High School graduation and 6 months experience or Associate Degree and three months, etc, etc, for the higher levels QC II and QC III, more time and /or education.
There is a lot more to know than just what kind of tolerance a bearing should have or how to do a blue check, its a lot of paperwork and study too, and getting to know a little bit about a lot of things.
I'm sorry to sound negative, but I don't know of any schools for a Nuc QC inspector. Maybe some of the large service companies will train their people into the position, like Ames or Westinghouse, but I don't know that for a fact. If I haven't totally discouraged you, look for the ASQ classes, and on your next job, ask the QC inspector what site procedures he uses to do his inspections. See if you can get copies and read them, it will give you an idea of what goes on. Because the Nuc industry is procedure drive (10 CFR 50 says you
WILL have procedures) Nuc plants have procedures for qualifying Inspectors. Get a copy of those, most places they aren't company proprietary information, so there shouldn't be a big deal about that. And good luck if you keep at it.
Oh, BTW, pay on the road for most QC seems to be in the $33 to 35 range, time and a half for OT usually, usual per diem (about 1/2 the federal rate for any one place)
and no retirements, 401Ks, or medical bennies.