I've had that problem, got a hennessy hammock and used it a few times woods-camping, I just tie up my dog to the tree the hammock's suspended by, but she usually ends up freaking out and getting no sleep because I'm up away from her in a cucoon while she gets to deal with all the night sounds alone, no good. I just use a two-tarp system right now, one above and one below, and it's the best, most versatile shelter I've used. Lightest as well, fuck I got tired of lugging around a tent/hammock that took up half my bag and most of the weight really quickly.
It's nice if your homebound and are going hiking for a few days, but for long term living I'd never lug around a hennessy hammock, tarps are the way to go I figure! That said though, I want to get a light, small hammock without the whole shelter gig going on for summer, just to have the option of lounging in a tree on a sunny day, they are definitely comfortable.