I work as a headhunter and have done so for the last three years. I expect I will continue to do so for the rest of my working life. Prior to that I worked in various business-to-business telesales jobs and a brief stint some years ago when I was new into the workforce at a "recruitment agency" that proved disastrous.
Recruiting is, in many ways, the most rewarding career you can choose, in terms of income and job satisfaction versus working conditions. There is no other job you can do which has a similar earning potential that doesn't require horrendous working hours, constant travel or several years of post-graduate education. This comes with big caveats, however - you have to learn in the right environment (90%+ of recruitment companies are awful), you have to be an incredibly disciplined, tenacious and resilient person with a faultless work ethic, as well as being emotionally intelligent and empathetic yet assertive, and many other things besides. It's an extremely difficult job and there are many, many FAR easier ways to earn a good living.
The reality is, only a small minority of people who try it out ever stick with it, and a smaller minority still ever excel at it. And it's really not worth doing unless you excel at it and reap the rewards of it. Think of it like acting - it's an amazing career for a few people, and a frustrating, uncertain, stressful hand-to-mouth existence for everyone else.
To add to that, it's never been harder than it is right now. Not only do third-party recruiting services suffer more than any other sector in a recession (indeed, 70-80% of recruiters leave the industry altogether with every recession), but the market is becoming increasingly commoditised and marginalised due to companies bringing their recruiting functions in-house.
I would absolutely not advise going into it straight out of university. Get some life experience first, and some experience in a more straightforward sales environment.