I don't have experience with acute kidney failure but from what I have read - if they think she can try to go off dialysis, and she's monitored carefully, she will find out if her remaining kidney can sustain her. The dialysis acts like a crutch, taking on some of the filtering that kidneys do, and perhaps the doctors hope that the infection or whatever damaged her other kidney has been treated and resolved.
It can take a year for the remaining kidney to grow larger and increase function (as in the case when a person gets a transplant from a living donor, both the donor and recipient's kidney grows larger.) Staying on dialysis too long can also have the reverse effect, where the remaining kidney loses it's residual function, because the machine is doing it.
Acute kidney failure can sometimes become a long term health problem which is called chronic kidney failure.
Here in the US your kidney function has to be below 20% before you can be evaluated to be on the wait list for a deceased donor kidney. The same criteria applies at most hospitals to get a transplant from a living donor.
Hopefully your girlfriend will improve and she won't have to worry about any of this. Best wishes to you both.