That's awesome, congratulations! My mom was in the Peace Corps and I always wanted to join (got rejected when I applied 8 years ago fresh out of college and have often thought about trying again now that I have some relevant experience). Mongolia was top on my list of where I'd been hoping to get sent, too.

I have extremely little experience with Mongolian myself, apart from a brief flirtation with it a while back out of pure curiosity, but I can highly recommend the forum at HTLAL for anything language-learning-related. I absolutely love languages and spend a good chunk of my spare time and money on them (trying to bring my Turkish up to scratch currently) - unfortunately I think my usual advice would be fairly useless for you given that a quick Google search doesn't turn up Mongolian versions of any of my usual go-to resources for starting in a new language. Unsurprisingly, I guess. Still, there do appear to be a number of possibilities out there, just none whose value I can personally attest to.

Good luck!