That idea rocks!
I've wanted to do something along those lines ever since I was a little kid (and I even grew up on a lake), though I must say I had something much larger in mind, say 2-3 acres or so. Also, not certain as to whether or not I'd stock trout; it would depend upon which part of the country the property was located in as well as the actual water volume of the lake and the forage available. The key would be to begin the newly-established lake by stocking it with dace or some other such baitfish, allowing the biological filter (i.e. bacterial bed and aquatic vegetation) to mature, then adding the gamefish the following year, or at the least much later in the season. That way, you are starting out slowly and building up without crashing the system. Of course, if the rate of water entry and exit from the body are high enough, you will in effect dillute the ammonia, nitrite, nitrate, and organophosphates quite effectively, which is great news to keep the system healthy. Also, remember that if the gamefish start breeding, you will probably want to remove some of them from time to time to keep the entire population from stunting (in the event that the food source is at its maximum). This is what's called "culling".
Either way, yes, permits can be difficult, however there is a way around practically anything in this country, and if government wants to dump sewage into natural bodies of water and drainage systems I think we all have the right to take a piece of land housing no endangered species and "create a lake" if we feel like it. I have a pretty extensive background in this sort of topic, growing up in the pine barrens of NJ and then college in Eastern SC (both wetlands areas) where lakes are created and drained by developers on a regular basis. To make a long story short, whether or not a mand-made lake or body of water requires supplementary water movement depends mostly on the topography of the area and the rate and source of water input into that body. There are ways to engineer such a water body so as to get all the water flow required simply by doing a little fancy work with a bulldozer or backhoe. Seeing as this is the sort of thing I do for a living (freshwater and marine chemistry, specifically as they apply to aquatic organisms), it wouldn't be too hard a project and I'd be very happy to help anyone if they had questions. Personally, I'd love nothing more than my own 3-5 acre lake stocked with smallmouth, brookies, and maybe a few pike.