Turn off the water supply according to your trailer's owner's manual. Disconnect the water line at the back of the toilet. Remove the old toilet by unscrewing the mounting bolts and lifting upward. Do not slide the toilet, you may damage the bolts. Remove the old gasket with a screwdriver and seal in a plastic bag for disposal.
Set the new toilet in the space, checking for fit. If the carpet extends under the base, trace around the edges with a water-based yellow marker. Lift and set the toilet aside. Cut the carpet with a utility knife and remove the scraps.
Install a floor flange adapter, if necessary, according to the manufacturer's instructions. Insert the new toilet bolts into the appropriate slots.
Attach a new gasket to the bottom of the toilet, with the lip side facing down.
Lift the new toilet and align with the mounting bolts. Set the toilet into place. Tighten the mounting bolts finger tight, then one-quarter turn more with a socket or box wrench, just until the toilet is solidly attached and does not move. Do not over-tighten or you risk cracking the toilet.
Reconnect the water line according to the manufacturer's directions. Flush the toilet and look for any leaks.