Birdseye Trail | Hoosier National Forest | Indiana Hike 

I don't think it's set up for camping. The Two Lakes Trail nearby is a good place for backpacking and camping.

I have camped there off trail. Dispersed camping is allowed throughout most of the Hoosier National Forest. Dispersed camping is acceptable on National Forest System lands away from developed campgrounds, nearly anywhere your camping equipment and/or vehicle does not block developed trails or road rights-of-way. It is not necessary to check in with the Forest Service when you camp overnight. Where dispersed camping is NOT allowed: within campgrounds along roads, parking areas, or day use areas within developed recreation areas at day use trailheads or parking areas, including boat launches within Pioneer Mothers Memorial Forest (Orange County) within the Hickory Ridge Lookout Tower site (Monroe County adjacent to the Charles C. Deam Wilderness) within Hemlock Cliffs area (Crawford County)