Is Fushigi Yuugi appropriate for younger children?

This all depends on what you allow your child to watch.
I suggest watching Fushigi Yuugi yourself.  
 However, I will tell you the basics.

In Japan Fushigi Yuugi belongs to a group of manga (comics) and anime called shojo.
Shojo is anime and manga marketed towards girls. It is normally characterized by
'low violence', delicate lines, feminine men, and lots of complicated relationships.

Fushigi Yuugi is about a junior high school girl who falls into the book of the four gods,
and becomes lost in ancient China. There, she is said to be the priestess of
Suzaku, one of the four gods, who with the help of seven celestial warriors can call upon
Suzaku for wishes. The plot seems lighter than it actually is, as in most shojo.

Throughout Fushigi Yuugi some darker points such as rape and suicide arise.
Also, there is nudity, and a sex scene or two (more artistically done).
The warriors all have tragic lives, and have to deal with the harsh realities of life.
Many characters die, which can be very emotional.

Fushigi Yuugi has many positive points
points about love, and friendship. These points are
stressed by other darker conflicts.

I would base this descission more on how
mentally ready your child is for these issues.