I don't want to sound even remotely apologist for someone like this, however given she believed what she was saying was a 'joke' and given she must not have realised it would offend her audience, I do view it as less hateful and more treatable than other forms of racism. I'd actually be more in favour of sanctions that re-educate or rehabilitate her rather than straight up firing her. Suspension would make sense even.
Walking out of the room straight to HR might seem like the right thing but confronting abhorrent views head on, person to person, with reason, is better IMO. She could have been shamed in to an apology on the spot.
A lot of you may not care about her, because words, but losing a job is a horrible thing - particularly when you have a family to look after. Do you want to change the world or just punish the wicked? Because I'm not sure making people destitute does anything other than harden them (and their loved ones) against all forms of humanity, including the ones they're already prejudiced against.