nok can mean many different things and can't always be translated with one word. In some contexts it means "enough" (and I bet this it the word you want to have in the English translation, isn't it?), example: "Nu er det nok!" = "It's enough now!"
But in this context it means something like: I will get a girlfriend, you'll see / in time. As if someone had just said to him/her: "You'll never get a girlfriend!" Get it?
Rather than "enough", I had "probably" in mind, and you lost your bet, here. But thank you for your complementary explanation and the idea suggested by "you'll see" / "in time". Therefore, "I will surely get a girlfriend", does it sound acceptable, or more in the meaning? Thanks to Mark for his explanation, too.
Regarding "probably": It is implied that the person speaking will get a partner (see above comment about "nok" having several potential meanings in different contexts, such as "in time", "eventually", "for sure"), so using "probably" introduces more doubt than certainty. Regarding "partner": I agree with you, since "partner" is gender neutral, as is "kæreste" (which might be more or less literally translated as "my dearest"). However, "partner" does/can have other connotations than bf/gf, eg. partner in a law firm, in a company, in sports (tennis partner), and it does sound rather formal (to me), if you are introducing you gf/bf as your "partner".
I wrote "Jeg vil få en kæreste." and it was also accepted. But wouldn't that mean "I want to get a girlfriend."? How is it different from this example: https://forum.duolingo.com/comment/14664485/The-place-is-going-to-be-closed