The divine nature or God doesn’t have qualia because he doesn’t have a body. It is simple as that. You are free to disagree. But then you have to define qualia as something completely different than what it is. So Jesus can not have 2 sources of qualia using the definition of qualia that everyone agrees on.
When we are apart from the body we can not have experience of qualia or sensory perception. But even then we are not like God who exists in a higher dimension outside of time and space. We would still be limited creatures of limited intellect. Apparently we are also aware of things going on around us. For instance the saints in heaven can ‘hear’ our prayers.