Is there a law governing what age opposite sex children can share a bedroom

No... there isn't. Not all parents can afford a place large enough to give each child there own room, nor can they be required to by law.

What type of housing is it? Private or government housing?

It depends on the housing and were you are from.

Such laws tend to be very localized. On the municipality level, not on a state or county level.

Generally they are part of guidelines from building or social services depts. They are generally not enforced unless uncovered as part of another investigation.

Why the question?

First agencies like CPS will have guidelines that they may try to impose if they are investigating you, so if that is the case, you will need to see what you local agency is demanding.

There are no state laws, and families with several kids and a two bedroom do the best they can.

Some apartment complexes may have their own rules that they will require.

Also government housing my again have agency rules for renting