You should consult your tax professional for tax advice.
There are two points in your favor:
The tax is based on the gain in value, and it is unlikely that there is a gain.
You are moving for a new job, so be sure to discuss the deductions that are available to you when you move
Lastly, check with your new employer regarding assistance in relocation. Some employers will help pay relocation expenses, including moving costs, re-connecting utilities, accommodations while you look for a new home, etc.
These relocation benefits may far outweigh any tax consequences that result from the sale of your primary residence.
Be happy for the little things. Most people that have held proerty for less than two years do not have a profit. And you are moving to a great part of the Country. And you are fully employed.
No you are not exempt from Capital gains, but the exclusion is not zero if you have help property less than two years it is a proprtional exclusion. The fact that you are moving to a more expensive area is something you need to address with your Company. There are tables that show the difference in living costs, try to leverage that in a higher salary.
And don't get tax advise from realtors or real estae advise from tax advisors.
Welcome to Boston.