Generic Collection copying method

I've got this useful little method that uses reflection to copy a single class instance. It has the advantage of letting you copy between classes that are not exactly the same, just copying the matching properties. I use it a lot.

public static void ObjectCopy(object source, object target)
{
    if (source != null && target != null)
    {
        foreach (var prop in target.GetType().GetProperties())
        {
            var FromProp = source.GetType().GetProperty(prop.Name);
            if (FromProp != null)
            {
                prop.SetValue(target, FromProp.GetValue(source));
            }
        }
    }
}

I've now got a requirement to do a similar thing, but with a collection, ie an ObservableCollection or List. I'm struggling to figure out how to do this in a generic routine. I can call the old routine from within the new one to do the collection item copying but handling the collection itself is what I'm struggling with.

Any ideas?