In general G1 hair is quite color fast unless exposed to UV (it will eventually fade, rate depending on the hue) or to chemicals, the most notable being OxyClean with the neon hair colors in particular.
I've washed more than one Paradise just using regular conditioner on both the hair and body fuzz - just stick to warm/cold water and you should be good. Extreme heat and rough handling particularly when wet can shred the flocking.