The little plastic cap that you described on the end of the hose is the standard way that breather tubes are terminated. The hose pointed to in your picture is definitely the breather for the rear axle.
Another poster mentioned extending it. I would second this suggestion as you don't want it to go underwater - you're likely to suck water into the axle housing in that case.
I replaced mine with a longer rubber tube and brought it across to the passenger's side and routed it up into the area behind the tail light. I had to remove the tail light to get access but it made for a relatively clean setup and the breather now terminates at a much higher point than the stock setup.
I also relocated the front breather to terminate on the firewall right at the top. I'd like to relocate the breather for the transmission (auto) and T-case but I can't find the bugger.
2007 2 door Rubicon. 3.5" RE lift, 35" Goodyear MTRs, Procomp 8179 15x8 wheels, 4.88 Superior gears and alloy shafts. Shrockworks stubby front bumper, Rockhard rear bumper, JE Reel 1350 driveshafts, Warn Powerplant winch, CB, GPS.