I certainly wouldn't be putting the wash water on the garden, even if it was just ornamental. Maybe the rinse water would be OK. Do you rinse the nappies before you wash (so by the time you get to the rinse cycle you already have gone through 2 loads of water)?

Anything that has been used in fertiliser has gone through a lot of treatment. It could have been subject to high temperatures or UV light to kill off the bugs.

Your council may have some guidelines, or the state health department. The things to keep in mind are possible pollution of ground water and health risks to people that come in contact with the soil. I am an engineer and am currently working on putting the sewer on to villages that currently are on septic tanks only which leak and have a local lake with very high faecal counts.

Yes cats and dogs poo in the garden - and give us toxoplasmosis if we come into contact with it!