I was/am in the same situation. I have a 1.1 cm nodule which is also cat 5 suspicious for papillary carcinoma which we were doing active surveillance on. It had been .9 cm last December, but it is growing so my surgeon recommended lobectomy.

After my diagnosis I researched a lot of doctors and found one that I really trust and click with. His opinion is that there is a lot of overtreatment when it comes to lower risk papillary carcinomas, and he favors going for the least invasive/extreme treatment that he believes will be effective. He, and every doctor I have spoken to (and I consulted several), stressed to me that even if they have to go back in at a later date to remove the rest of it, the ultimate outcome will be the same. For a cancer like this, he assured me that I am not risking my survival by opting for lobectomy now. I guess the main downside is having to potentially go through more than one surgery (and face the risks associated with any surgery requiring anesthesia) and also with the lobectomy you can't monitor thyroglobulin levels to potentially detect recurrence.

So, I feel very comfortable with a lobectomy. There is a good chance that this could be (mostly) in my rear view mirror in a few months (my surgery is May 2). There's a good chance I will not need hormone supplementation. I like that there is less risk of recurrent laryngeal neck palsy and hypoparathyroidism.
Regardless of removing part of full I will be checking it for the rest of my life. But with the partial I feel like there is less potential risk to my quality of life and, fingers crossed, it may never pop up again. Trying to balance optimism and being realistic about the possibility that it might.

Everyone is different and there are so many factors that determine what action is best to take for the specific case/individual. I've been told by more than one doctor that in cases like mine there is no absolute right answer -- they defer to us to decide what we feel most comfortable moving forward and living with. I like to think that they wouldn't give us the option if they thought one of the routes was a bad decision.

Best of luck to you!