How quickly do I need thyroid surgery when a 1.1cm nodule has been biopsied as probable papillary carcinoma? Thyroid hormone levels normal.

Within weeks. It should be removed within a reasonably short amount if time, but it is not an emergency. Don't put it off, but also don't be concerned if it can't be done in a week or two.
Timing. There is no urgency however in my practice , and other doctors as well i assume, once a diagnosis of cancer, or probable cancer, has been rendered there is no advantage to waiting for surgery. Likely there will be significant change if done in weeks to a few months, but there are of course no guarantees. Do it when it is the least inconvenient as soon as you can.
Soon. Take the time to find an experienced thyroid surgeon. Complications increase when the surgeon is less experienced. In your age group most would recommend a total thyroidectomy for papillary cancer (you may need an intraoperative frozen section - so the skills of your pathology department are also important). Management of lymph nodes in early papillary cancer is controversial - get an expert!