I don't understand why your doctor would tell you to go back to eating meat to get your B12 levels up when even B12 supplements will not help.  Most people who have a B12 deficiency can not absorb B12 from foods or supplements and need to take injections for life.  I would find a different doctor if I were you and get a second opinion. 

That said, I am only 40 but I am in surgical menopause (lost both ovaries) since 2005 so I know all about that.  It took me three years of hell before I found a hormone replacement (bioidentical) that helped me feel human again.  I also have thyroid issues (23 years ago I was diagnosed with hypothyroidism) and balancing the two hormones can be a challenge since they oppose each other.  But eating a whole foods clean vegan diet (going on 20 months now) and exercising very regularly and vigorously has really helped me a lot.  I recently had my iron, vitamin D, B12 levels checked to be on the safe side because I was having thyroid related symptoms and tested for that so they threw in the other tests for peace of mind.  All were perfect and this is after 1 year 8 months as a vegan.  So I can attest that a vegan diet works well if you are mindful of what you eat.  I include a MINIMUM of two cups of leafy greens every day along with a food source of vitamin c and also legumes, beans, and a tablespoon of blackstrap molasses daily for iron and calcium.  Iron is another area that can cause hair loss if you are not getting enough.  A plant based diet provides plenty but be sure to consume vitamin C rich foods with it.  I also include two to three servings of whole raw nuts and seeds or flax oil daily to my diet for the omega 3s.  Walnuts and flax oil or seeds are especially important as they help the body convert ALA to DHA.  Vegans do not have an adequate direct source of DHA but there are DHA supplements derived from sea vegetables (where fish get their DHA) that you can take if your body does not efficiently convert ALA.  My hair is very thick and my nails grow fast and strong.  Since upping my nut/seed intake I have had to trim them more often. 

Also have your thyroid checked to be sure this is not causing some hair loss.  Hypothyroidism is notorious for causing hair loss.  Lack of estrogen and other hormones can also cause the hair loss.  I have not had an issue since being on hormone replacement.  I need to take it because I am still young and suffered dramatic bone loss when I lost my ovaries. 

How did you manage menopause as an omnivore?  My guess is that your hair loss is due to something else if you are just noticing it now.  I have done very well as a vegan but my Mom went vegan six months ago and she has lost a lot of hair as well.  She also eats gluten free and limits her diet more than I do so I suspect she is missing out on some nutrients and not eating enough.  She only used olive oil for her fats until I told her to include the nuts/seeds and flax oil in her diet.  She started taking a DHA supplement recently (DEVA brand online has them for vegans).  I will report back if it is helping her. 

One other thing.  I do not use commercial shampoos and chemicals in my hair.  I use only pure vegetable soap and pure tea tree and lavender essential oils for my hair diluted with water.  I have done this since going vegan in February 2011.  I think getting the excess chemicals and alcohol out of my hair that comes in shampoos helped.  I also eat a ton of fruits and vegetables every day.  I do not consume soy at all because it blocks the action of my thyroid meds.  I cut soy out of my diet about three months ago.  Soy can help with menopausal issues though but if you are on an hrt already it can interfere with that.  Natural organic soy such as tempeh or organic tofu (not the processed soy in milks and other products) might help with menopausal symptoms but it can also make them worse.  Play around with that too and see what happens. 

I am one that will not take one doctors word on something.  I do my own research and get other opinions and I have been known to seek out more than one doctor on an issue.  The last time I trusted one doctor to tell me what's best for me I woke up after a hysterectomy with both ovaries gone to my horror.  I was 33.  Definitely get a second opinion and make sure you get a physical copy of all your test results so you know what was done and how to interpret them.  Go to the PCRM website and email those vegan friendly doctors and get their opinion on hair loss also.  It might help direct you in what to do or where to look for answers.  Good luck!