I've taken my golden retriever on a few hikes. The best method that I've found so far has been to take along an appropriately sized permethrin-treated CCF pad to place on the ground under the hammock. She seems quite content to sleep on the pad, and I connect her leash to one of the support trees to prevent any wandering temptations.
“I think that when the lies are all told and forgot the truth will be there yet. It dont move about from place to place and it dont change from time to time. You cant corrupt it any more than you can salt salt.” - Cormac McCarthy