You have a short window of opportunity, between diagnosing B12 deficiency, and the damage becoming permanent.
Once you have been diagnosed with B12 deficiency, there is no reason to hold off taking treatment. The only reason to hold off getting treatment is if you're still waiting for a diagnosis. Once you begin to take additional B12, then it is difficult to do a blood test and get a confirmation of B12 deficiency. Of course, if your doctor has already taken a blood sample for the tests, then you can begin taking B12 straightaway.
B12 is a food substance, and there are no side effects from taking it. If it turns out that you are not B12 deficient, then your doctor will need to give your other treatment. But it won't have done any harm if you have already started taking B12.
If you want to know about the medical literature that supports this, then please check out BMJ Best Practice (this is the section on the British Medical Journal web site where they summarise all of the research so that a busy doctor can take a subject in). It's a subscription only web site and restricted to medical professionals, but you could ask your GP to print off the relevant section to let you read it.