I think a question you need to ask is Will the current battery work for the next three months? Is it just time to change the battery, or is it currently failing to produce enough energy to start the car? If it can wait for the three months, my suggestion is to just wait.
A battery, whether new or old, if to let sit idle, will lose charge over any given length of time. If left long enough, permanent damage may occur to it.
Whether or not you decide to change out the battery, the best thing you can do for your battery is to put a "battery tender" on it. This will keep the battery fully charged and in tip top shape without fear of sulfation (sulfur crystals forming on the lead plates) which can happen when a battery is allowed to fully drain of its charge, which may happen if left to sit too long in a vehicle. When I say a battery tender, I'm not talking about running your battery charger on it at 2A, but rather, there are specific built tenders which will provide just the amount of amperage the battery needs to maintain it all the while checking the battery to ensure it is fully charged. These are a lot cheaper than a new battery and do a great job of keeping it fully charged.