Is it good to be well-rounded, or does that just look flaky?

I'm in the middle of a career transition right now. I'm working on a Master's in a field that is totally different from what I did before (going from business to software engineering). I'm also about to move to a new city, so I'm looking at this move as an opportunity to do something different.

Here's my problem: at the moment, I'm not qualified for software jobs. I won't be for a few years, and I don't have experience in networking or other IT-type jobs. It would be really great if I could land something that would make the transition easier, but that looks pretty unlikely, and unpaid internships aren't an option for me (I need income).

Does it make me look flaky if I seek out a job in a totally different field while I'm finishing grad school? I'm making the transition away from business/finance for a reason - I don't enjoy it anymore. Do employers frown upon resumes that seem jack-of-all-trades-ish, or is it good to have a well-rounded career history?