I can't speak for your local roads, but there are plenty of regional roads that are reasonably safe for a youngster to ride on, especially when accompanied by an adult. Even more so if the adult is an experienced cyclist who can pass along some tidbits of road wisdom.

So, in general, you should be able to expand the horizons.

However,

This is a delicate situation because she's not your child. She's a grandchild, so it's critical that her parents make an informed decision about this. Otherwise the potential for family grief is unacceptably high should even something minor go wrong.