Sounds like your doctor has things under control. Make sure your bloods are tested regularly, I became hypo after one month on 20mcg followed by two months on 40mcg. I was ok when my bloods were checked after the first month but no one checked again until I'd been on 40mcg for two months - alas too late I was hypo. So don't sit on 40mcg for too long without getting your bloods rechecked.
Try and get your B12, Vit D, ferritin and folates checked too. When you get the results back you want them to be in the top half of the range, even if the doctor / endo says they are ok.
When I started on Carbimazole my pharmacist came out specially to tell me to be sure to take Vit C along with the carb so it might be worth doing that. I still take 1000mcg + zinc.
Make sure you get and keep copies of all your test results. I also kept notes on how I felt throughout my treatment. I had a little notebook marked out. So that I could ask the endo at appointments what my results were ( for my records)
I also wrote down any questions I wanted answered and how I was feeling etc. I think it was good because it let everyone concerned know that I wanted my treatment to be a partnership between me and the medics rather than handing myself over to the hospital and letting them get on with it.
That way I knew how my body felt throughout the treatment, helpful when I. Had to fight for any changes in my doses - I was being treated with block and replace (ive got Graves - hyper with antibodies) and needed regular increases in levothyroxine.
Good luck, you've come to the right place for support and advice.