If you truly want to only go 3 miles and be away from people, Yosemite may not be the place you want to go. There may be a lot fewer people in September/October but there will still be quite a few visitors to the park.
It will be cold, and most services in the park will be shut down. In mid-October you will not be able to park overnight on Tioga Pass, so a short backpacking trip will probably need to start out of the valley or another location such as Hetch Hetchy. That late in the season winter weather starts to show up, and while it is unlikely to dump several feet of snow, there is a pretty good chance of at least a few inches of rain and snow, so you will need to be prepared for storms and below freezing temperatures. Another consideration may be the chain requirement - snow chains or cables are required around the time snowfall is likely, and I'm not aware of any rental cars that will let you use them.
Most hike-in camping spots starting in Yosemite Valley will require you to hike uphill (steeply in most cases) and more than four miles on your first day. Camping along the rivers tends to mean you need to be four miles from the trailhead. Fires are only allowed below 9600 feet in elevation. Fishing in the Merced is catch and release only in a major part of the river. You will want to look up California fishing licenses and regulations before going to the park so you have the correct lures and know whether your destination will allow you to keep the fish you catch or you will have to fish with barbless lures and release the fish.
Have a look at the yosemite website on wilderness camping/backpacking -
http://www.nps.gov/yose/planyourvisit/backpacking.htm - and read about the various trailheads and the regulations for food storage and wilderness camping. You will need to fit all your food and trash and any items that have a smell to it (toothpaste, soap, any cream or powder, anything with a scent) inside bear canisters.