I would not say it's certainly foreign. It's unlikely, for sure, that there would be an established word for such a concept.
1) AFAIK we don't know that there isn't any strange cultural niche for female warriors (or has GRRM explicitly denied the existence of such?). From what we know it does not seem likely, that's all. For example you would not expect there were female samurais, but there were. We know that Dothraki women can sidestep or transcend their usual place at least by becoming Khaleesi and then part of Dosh Khaleen; perhaps also by becoming Koalakeesi. While they seem generally to fall on quite familiar "support and nurture" role, they don't seem to be expected to be passive or timid, if I remember right. I would find it only moderately surprising if there was some way for woman to become a fighter in some culturally aknowledged capacity; outcast, defender what have you.
2) Dothraki can have words for phenomenons of other cultures. There's a chance that in some nearby culture female fighters are more prominent. Dothraki are kinda glum isolationists, but they are also damn remarkable travelers - in a world where most people pretty much sit where they're born, scarcely moving ten miles ever. Granted, Dothraki's contact tends to be limited and often violent, but they do have even this extortion-flavoured trading system. And since they fight a lot, fighting related concepts should stick easily and travel fast. Maybe their tales would not be of brave woman warriors, but of cricket men who let their women do the fighting, yet the word might still get established.
3) It's not even absolute necessity that there were any real woman warriors. Dothraki have their legends - probably a huge pile of them. And one thing that often crops up in legends is world-turn-upside-down scenarios. You can have words for amazons and unicorns. And then when you travel to strange lands and meet such crazy mockery of natural order as woman warrior ... hey, how lucky is it that you already know what to call them.
And whn it comes to King Alan's needs, the question seems to often be, what words would Dothraki (or Daenerys speaking Dothraki to Dothraki) make up on the fly when they'd travel across the Narrow Sea and meet new things. You'd expect a lot of rough, loose word compound expressions in line of lajak eveth. But Dothraki seems to compound/derive easily, so some proper comopounds and derivations should be quickly established. And of course there would be a couple of more creative, rules-breaking coinages, like lajakeesi (if /-eesi/ is indeed calcified or otherwise not strictly eligible) ...
