What would be the consequences for refusing confirmation in the Anglican Church? What would be the consequences for a teenage child of committed Australian Anglican parents who chose to refuse confirmation?

The confirmation may be refused either before the ceremony, i.e. refusing to attend, or during the ceremony.

I'm interested in what church doctrine would say as to how to deal with such a person.
Most(?) Anglican churches probably run confirmation classes. If anyone had solid reasons to not want to be confirmed those reasons would arise during the classes, so if they changed their mind right before the confirmation itself then that would be an impulsive decision, so I don't think there's much point looking for any regularities about that.

What about if you express your desire to not be confirmed earlier? Well Anglicanism is very diverse. Some churches will make a big deal out of confirmation, others less of one. Some churches will think of it as a rite that everyone goes through, others will not. Some will pressure the youth into doing it, others will wait for their youth to ask to be confirmed.

As someone who attends an evangelical Anglican church, I think it would actually be a good sign that someone did not want to be confirmed: it is very unhealthy for churches to confirm people who really have no true faith and confidence in God. To say "I shouldn't do this" is a good thing to say. Whether they are having doubts or are a firm atheist, it is much better to not be confirmed than to confirm people who aren't true Christians.

If someone is willing to talk through these issues with the leaders of their church there is unlikely to be any long term consequences. Many dioceses however will not let you do certain things in church services without being confirmed, but if you don't want to be confirmed it's unlikely your church leaders will want you to service lead etc anyway.