Hi and welcome to MM
Do get your GP to do some blood tests - these are not always reliable but can be an indicator. Diagnosis of peri menopause should be done from symptoms really. You don't need to have the Mirena removed to see if you are menopausal or not the FSH level is a better indicator and/or the emergence of menopause symptoms.
If you are over 40, getting flushes or any other menopause symptoms ( see the list on this site) then you could have the Mirena changed (do get another fitted anyway) and add in some oestrogen as patch, gel or pills to control flushes etc. If you get on with the Mirena well, then it's ideal as part of HRT treatment, both in peri and post meno, you just have to have it changed every 4 years and add in oestrogen as needed alongside. DG x