Welcome to a life with Diabetes.
I am tagging
@daisy1 as you may not have seen the welcome information. Read it and absorb all you can.
There is no average time for lowering but there are various ways to do it. Not as simple as "How do you do it?", and no quick fix .. in fact, very rare for a "fix" but a plan to lower and manage instead.
You mention a low carb diet ... what do you consider "low carb"? What do you eat?
Are you using any meds to lower your levels?
Are you overweight?
Have you seen an Endocrinologist or just your doctor?
If diagnosed just before Christmas then your journey has just begun
15.1 is high, especially if consistent, and definitely needs to come down a lot - but when do you check your level? How often?
Be detailed in your next post and be prepared for a diet change, lots of information to educate you on Diabetes, and of course plenty of advice.
Lots of help here with many "life-timers" to help guide you.