As an ex-floor covering installer, please, for the love of god, please, put down some type of tile. If for nothing else, for the poor bastard floor covering installer that may have to replace it at some point. I know carpet is more comfortable, but you have no idea how nasty it is to have to pull pee stained carpet up from around a toilet. There are also structural reasons, such as carpet will hold moisture and cause the floor to rot out quicker, where vinyl or even ceramic will seal the floor and protect if from the moisture, but that really isn't even close to the top of my list, the first five reasons are this....
1. Pulling up nasty pee stained carpet sucks.
2. Pulling up nasty pee stained carpet stinks.
3. Pulling up nasty pee stained carpet is nasty.
4. Pulling up nasty pee stained carpet is digusting.
5. Pulling up nasty pee stained carpet sucks.