Adding a propane powered water heater outside your trailer is easy. My uncle had a 40 gallon plumbed into his trailer at his seasonal site. You simply need to tie the inlet of the water heater into your cold water supply line, and the outlet into a hot water line. You also need to supply fuel to the water heater. All three of these connections could be made inside the existing water heater compartment.
That said, you'll probably want to use a flexible supply line to and from the water heater, and add fittings onto whatever plumbing you have in the trailer so you can connect said supply lines in. Some kind of shut-off would be good too so you can use the water in your trailer when you are disconnected from your water heater.
This wouldn't be what I would consider a "My First RV Mod" project. The water is easy enough, but propane is one of those things that can go boom.
You are probably better off repairing/replacing your current water heater. If you are handy enough to tackle adding an external water heater, you are handy enough to replace your own water heater. New units can be had for under $300 on Ebay or PPL Motorhomes
http://www.pplmotorhomes.com/parts/rv-water-heaters/60154.htm.