I wouldn't get it anywhere near the eye area, it is likely to sting and irritate.

A good way to introduce it is by using it once per day at night every 2-3 nights instead of the usual moisturizer. Give that a try and see how your skin likes it.

So I should avoid AHA below the eye right?

AHA is used for exfoliating the skin so you should avoid applying it under the eyes. The AHA will tighten your pores and reduce black heads but it will not remove the dark circles under your eyes. Dark circles are usually caused by lack of sleep or dehydration. To remedy this, I would suggest that you drink plenty of water, get adequate sleep and cold compress on the eye area. If all else fails, you could use a concealer.