I've been through multiple cycles of IVF and have 3 kids to show for it. I was not in perimenopause at the time (although I likely am now). My understanding is that as you get into perimenopause, your FSH levels rise. This will impact your ability to ovulate and the number of eggs produced per cycle, perhaps also the quality of those eggs. I do not know how your doctor knows you are in perimenopause, or if s/he is referring to another earlier stage I do not know about.
The perimenopause issue is something a reproductive endocrinologist can sort out for you. I'm not sure what doctor you spoke to or his/her specialty. I would highly recommend you see a reproductive specialist, perhaps an endocrinologist or perhaps one specializing in genetic disorders. It certainly doesn't hurt to have a game plan in mind for the future.
I can tell you right now that I believe I am perimeopause, and I still ovulate. Painfully sometimes, too! So being perimenopause does not mean you cannot still have kids. You have heard of those "change of life" babies women have in their late 40's and 50's? It can happen.
If you want more information, please feel free to send me a private message. There are other resources I can share with you.