I got a job offer shortly after starting my PhD. So my question is: What should I say to my advisor about why I am quitting my PhD? Is it fair to tell her that I have accepted a job offer? And What should I say to an employer about why I am leaving my PhD? Will it not cause them suspect that I can't survive a PhD, let alone a job with them?
This is pretty common in my field (applied math). Students see the amount of money they can be making, and see the amount of work a PhD is, and leave. Be cordial about it, but the institution (and potential adviser) will likely be very unhappy. Make sure you are confident in your choice before even mentioning it to your adviser. Because of this being a common issue, I know that for plenty of professors the moment you start speaking about industry you have already burned the bridge.
As for what people in industry will think, I can't comment for them. Some will probably think you made a good conscious choice to not continue pursuing a PhD (just tell people about how the job market isn't that good). Others will think you dropped out.
This is just such a personal thing. People will see it how they want to see it no matter how you tell the story.
Chris's comment is spot on. Some other points:
Aside from people being unhappy, you will be faced with a lot of pressure from your advisor(s) to remain in academia. In my experience, professors view it as a mark of personal failure when one of their students leaves academia for industry. Some of your classmates may respond in this manner also. It's always your choice whether you want to engage in conversation, listen to their points, or simply just say "this is my choice and that's that", but you should be aware that the conversations will happen.
People in industry likely won't care either way. That said, it will be in your best interest to have a good reason why you're leaving. Simply saying "I had a chance to earn gobs and gobs of money" doesn't look good on you. Likewise, any sort of complaint against the program ("didn't like the research", "didn't like the advisor", "too slow") is bad. Your stated reason typically should include (1) interesting topics in industry, (2) personal demands (spouse was relocating), or (3) opportunity too good to pass up. Be optimistic about everything.
If at all possible, stay on good terms with people in your academic department. Wherever you're going, you'll eventually be in a situation where people will need to be hired, and knowing people in the university can give you an early look at graduating students looking for positions. Don't consider this a burned bridge; try to leave on good terms, if at all possible.