No, and no headhunter is going to touch you with 3 years experience in that industry (they do touch other sectors at that experience range, and at much lower fees, but not ever energy) Headhunters are used for hard to fill positions and get paid hundreds of thousands of dollars. Why would an organization pay crazy money to find someone when they could just use a recruitment firm or advertise themselves.
Plus what sector of energy are you looking at? Nuclear, wind, solar, good vibes, fracking, coal...?
For profit or non profit?
Energy is suffering from a lop sided market right now, so many candidates for so few jobs, therefore a firm would not need to pay more than the 300 dollars to post a job on indeed or wherever. Firms only ever pay when they can't find good candidates themselves, or are lazy.
However, if you can pin down a headhunter and they like you they will shop you around for free (no charge to the employer) this can be very useful and is a tactic I use when looking for good staff all time. We pay big money to headhunters and if I need a good junior or mid level person I ask them to keep their ears open, they are deep into the sectors and know a lot of the ins and outs of organizations. Up to you to impress them however, and that is the hard part.
Recruitment firms are different and market themselves in two ways, temp to hire or straight up perm placement. all are options, sometimes good, sometimes bad. For example, say you register with a temp firm and they market you out in one of their annoying weekly emails (spam) then you apply separately, with knowing you have been marketed out to one of the same organizations, then that recruitment firm could have a legal challenge to charge a fee to the organization that hired you ( this would never hold up when challenged in a court) but it can make organizations skittish and that's the last thing you need. So pick your agency carefully. I.e. Not randstad or the like.
My advice in order of statistical chances of landing a good job in your preferred sector is: old school applying for jobs / networking / volunteering /
Don't worry about taking the bd job while you look for dream jobs, even if you have only been in bd job for 6 months and get your interview with energy llc, just tell them the truth.
Good luck, finding a good job you love in a sector you are passionate about it a full time job in itself! Don't give up, get good feedback (I.e. Not the fucktard degerates that populate this cess pool of a sub).
Finally finding said job is, at the end of the day, a statistical process, and you have full control of all the variables.