Both are correct and natural. For more explanation: "For" indicates purpose. I am going to the store for milk. I am going for milk. "On" indicates an excursion. I am going on a fishing trip. I am going on a hike. "going verb-ing" indicates an outdoor recreational activity of variable duration. I am going hiking. I am going camping. I am going swimming. I am going bicycling. special case - I am going shopping. [correct and common]