I'm assuming that your neuro knows about the rabies jab? If she does and isn't concerned, then I guess it can't be related. If she doesn't, then she really should be told (and before you have a booster). Please note, I do not know of any reason why it would trigger demyelination, but it seems to be rather unfortunate timing, as you said.
As Tina has already said, to be diagnosed with MS, you need to show that there has been more than one attack. This means either a new relapse if you have RRMS (relapsing remitting MS) or at least a year of progression in symptoms if you have PPMS (primary progressive MS). They really can't budge from these rules even if they "know" it's MS because, although it seems unlikely, some people do just have that one attack and never have another.
It is possible to demonstrate a new attack by having a new lesion on MRI, even if the patient has no new symptoms. This is because a lot of MS lesions are what is called "clinically silent" - in other words, they don't cause clinically observable symptoms or signs. But a new lesion irrefutably means new activity, i.e. a new attack.
I don't know why your neuro won't do another MRI (budgets???), but I guess ultimately it comes down to the fact that MS just isn't an emergency and even if you were to be diagnosed following a new MRI, you wouldn't be eligible for DMDs because you wouldn't have had two "clinically significant" relapses in two years. So, in her mind at least, there's no rush.
Frustrating as hell for you, but she's taking the sensible approach.