He Said/She Said - Long-Distance
Not a chance. And here's what you and your girl are going to do: break up.
I would really, truly love to give you something more uplifting than "you're screwed," but years of military deployments gave me all the experience I need to emphatically conclude that distance only equals disaster. You will both appreciate the honesty and maturity of curtailing it now, instead of taking the next couple years to drift painfully apart as you inflict agonizing misery on each other in a childish attempt to preserve your long-distance (read: imaginary) relationship. I'd love to wax poetic about how, if your love is real and strong and true, then "distance makes the heart grow fonder" and that "love knows no bounds." But in reality, your long-distance (read: imaginary) relationship has far less tender proverbs of its own: "Out of sight, out of mind," "time heals all wounds," and "a bird in the hand is worth two in the opposite freaking hemisphere and is significantly warmer to the touch." Get your head out of the clouds and deal with the reality of your situation. Realize that no Hallmark-card, candy-ass sentiment will save you from your solitude – that the heat of another human body will always trump the warmth of fond memories.
You're an adult: There's no such thing as Santa, there's no such thing as unicorns, and there's no such thing as long-distance (read: imaginary) relationships that work. What are you, five?
Now that we're not playing make-believe, let's get very real here, cabrón: I don't know what excuse you told Stacey-Stuck-Stateside to justify leaving her in your self-righteous dust while you went gallivanting around the planet for consecutive years at a time – voluntarily! – but you're not volunteering to dig irrigation ditches for poor families in Jordan, you're spreading your humanity in South America, the Fertile Crescent of caliente, and your "charity work" consists of private English lessons for ambitious, young Latinas who will be muy agradecida to have you help develop the suavidad of their lengüetas.
The question isn't whether or not you can make your relationship work; the question is why would you want it to?
Suffering through a long distance relationship is never worth it. How well established can your relationship be if it's only two months old? Probably not well enough to last through a 27 month-long separation.
How well do you know this person? Have you two established a strong enough level of trust to not be worried about someone being unfaithful? These are the kind of questions you should be asking yourself before you make this decision.
You are very courageous for joining; don't make it harder on yourself by bringing along your excess baggage. Communication will be hard because your resources and time will be limited. At some point during this time both of you are going to crack, it is just a matter of when.
In my honest opinion, long distance relationships never work. It usually has something to do with the lack of physical contact from the other person, but it could be for a number of reasons. Talking on the phone can only do so much, and even if you can video chat, the paranoia of not knowing whether your partner is being faithful or not is enough to drive anyone crazy.
You are going to meet some awesome people and go on some incredible adventures. Whoever is waiting for you at home will only feel left out and alone while you are gone. The best thing the both of you can do is put your relationship on hold.
Enjoy yourself while you are gone, and agree on a time or place to meet when you get back. That will be the perfect time to reevaluate where you both are in your lives and decide what you want to do from there.
Other than that, the Peace Corps website offers a lot of information from past and current volunteers about how they communicated with their family and friends, as well as how the experience changed their lives. The best advice you can get for this question will probably be from them.