Your dose may change in the future; thyroids can slowly deteriorate. I'm 5'2 and between 8 and 8.5 stone, 125/150 alternate day dose works best for me. I never put on much weight; in fact when very under I loose it as you loose muscle. When getting better I bulk up a bit then later on the fat gradually eases without hugely trying.
Base TSH on how you feel; if in 3 months when tested you feel much better and TSH is 1.5 that is ok for you for now - your thyroid might still be producing some of its own. However it's likely that in the future it won't and then you'll feel best at lowest TSH, certainly below 2, generally 0.3-1. It's explains this in the book I mentioned.
It could be worth asking to be screened for coeliac, but many people do notice a difference without gluten.
Of bigger importance imo is vit d, ferritin, b12 and folate. Do you know if any were tested? You should be able to ring the surgery and request a print out. These all need to be in upper ranges, ferritin above 70 at least. I've been very ill due to lack of ferritin.
I'd be kind to yourself about the calories, low thyroid affects muscle strength. Proximal muscles to be precise. Your muscles will be a bit weaker and we need the calories to help recover.
Health unlocked have an excellent advice forum, very knowledgeable. iirc I think one post once said don't cut out all the carbs as they are needed for muscle energy and serotonin. From my own martial arts training, yes extra protein is good but I needed the carbs for energy.
I think this is why it's so important to have good ferritin and vit d particularly; as both aid muscle growth and recovery.
Thyroxine is not a complete treatment, as explained in the Toft book. There will be times when you feel crap and need dosage adjusting, but it's then (I've learnt to my cost) that the ferritin vit d etc need checking. You are now entitled to free prescriptions too, as it can be for some quite disabling.
I think regular exercise really helps for the usual reasons, but also as it really helps you notice when you are struggling. But if you are, do be kind and ease up (I haven't in the past again to my cost).
I also find I'm more anxious when a little under - I think you know you're struggling.
It can really affect memory and from what I've experienced, working memory and the ability to multitask.
Also - you will need extra thyroxine if you become pregnant in the first trimester, this is clearly in the nice guidelines, but not all gps know.