Tell her 'gosh you hate it here so much, I really hope you can find another position asap. Me, I'm staying, and I don't need to be depressed and demoralized, so keep it to yourself. If you plan to stay, suck it up and enjoy it.' Tell her this over and over and over and over. If she deep-down wants to leave it may push her to do it. If she keeps staying and whining, get her 'written up' with the boss several times so he/she/it is aware she is a genuine workplace nuisance.

With luck she'll decide you're an enemy and leave you alone, or the powers that be will eventually 'downsize' her, or a miracle will make it dawn on her that her whining is a genuine problem. AND IT IS, make no mistake. If you're having problems seeing yourself staying there, and you're an asset to the staff, then she is a genuine problem.

Been there, done that, have had three very normal, nice, but poisonously negative colleagues destroy morale in three different firms, because THEY had one foot out the door...we were stuck staying after our eyes had been opened to all the dirty laundry and negatives in the firm had been beaten into us.....poison, human poison. All you owe them is to tell them you don't want to hear it, and they're too damn insensitive to figure it out unless you do tell them very bluntly.