Eyebrows are perfectly safe to have done. Believe it or not the original electrolysis treatments were done on EYELASHES! (These were done in galvanic electrolysis by the way.)
You will find that although your first eyebrow appointment may be on the long side, you will quickly come to the point where you are spending just 15 mins every 3 weeks or so to keep it up, and then once every 3 months, and soon not at all.
I would suggest first having your brows done by a professional eyebrow shaper (plucker, not waxer)so that you have the exact perfect shape that you want to freeze for all time, and only then go see your electrologist a few weeks later. This way the only expertise you are asking of the electrologist is hair removal, not shaping.
Eyebrows get some of the best results in electrology. You will soon just wake up every morning with that Superstar look.