And to answer OP's question, if Ellie ever has kids (which I doubt would happen due to her infection and the world of the Last of Us), they would not be immune. Her immunity (if you'd even call it immunity) is due to a mutation of the cordyceps that stemmed its growth inside her brain. Her immunity is in no way genetic.
That's real smart of you. Say spoiler alert, then put the spolier in the title for everyone to see....
Good job man.
Considering you find out about her immunity in practically the beginning of the game, don't see the problem.
Change is the law of life. And those who look only to the past or present are certain to miss the future.
- John F. Kennedy
Wait but didnt Ellies immunity come from a mutation in the cordyceps, and not genetic? So wouldnt her biting someone actually sort of make them immune? Or am I missing out on something?...
Ellie is infected with the cordyceps in her, but the actual fungal growth has mutated somehow due to unknown reasons, causing her immunity.
So unless every other person she infects gets their codyceps mutated too, they won't be immune.