I'm not sure if this is the best place to use Insert Rules.
However you can use item:created
event instead:
<event name="item:created">
<handler type="YourNameSpace.UpdateFieldEventHandler, YourAssembly" method="OnItemCreated" />
</event>
public class UpdateFieldEventHandler
{
public void OnItemCreated(object sender, EventArgs args)
{
using (new SecurityDisabler())
{
ItemCreatedEventArgs arg = Event.ExtractParameter(args, 0) as ItemCreatedEventArgs;
if (arg != null && arg.Item.TemplateName == "Your Template"
&& arg.Item.Parent.TemplateName == "Your Template")
{
arg.Item.Editing.BeginEdit();
arg.Item["Your Field Name"] = arg.Item.Parent["Your Field Name"];
arg.Item.Editing.EndEdit();
}
}
}
}
Code is not tested but in worst case it should point you in the right direction.