It's hard to say without knowing more about your background, but many have done it before. A degree in econ is useful but by no means necessary.
You should probably worry more about your math training (have you taken real analysis or another course with real proofs?) than your econ training. I had three calculus classes and linear algebra. The first week of classes the professors were talking about quasiconcavity and the Bellman equation. I was lost. I worked 80-90 hours a week the first year in order to catch up.
"Also, it seems to me that the general market for energy economists is very strong, and will remain that way for quite some time. Do you think that's accurate?"
I have no specific data, but yeah, the market for economists in most fields is strong. Our program is not highly ranked, yet almost all of our PhD's are able to get tenure track jobs with reasonable teaching loads. To my knowledge environmental/energy policy is a hot field right now, particularly if you can bring in grants.
"as far as I can tell economics is the field that most closely aligns with this in the context of energy and the environment"
You should also consider PhD programs in agricultural economics or environmental economics. Highly-ranked economics programs often have a theoretical/mathematical focus that doesn't fit with what you want to do. I know from experience that energy isn't fully respected in economics departments.