I don't know how difficult it is to bring a foreign domestic helper into Mongolia, but I know it can be done. I know a Filipino woman who was working as a nanny in Ulaanbaatar, who I had talked with every so often when taking my kid to the local playground last summer. I do know it is becoming a little more common for well-to-do Mongolian families to hire English-speaking foreign nannies or helpers. So it is possible, though I'm afraid I don't know the process. My limited understanding is that the domestic helper in question will need an HG work visa, though one needs a Mongolian company to submit that visa application. Maybe the company giving you the job offer can help with that; if not, it should not be hard to find a local domestic helper (though one with more than a partial proficiency in English may be harder to find, or expensive). Alternately, there probably is one or more Mongolian agencies that specialize in hiring foreign domestic helpers. Many Mongolians seem to be quick to find and take advantage of business opportunities, so I find it hard to imagine there's no such agency there yet 
Here's a couple links that describe visa requirements for living or working in Mongolia: