In Chapter 8, Winston sees the dark haired girl (who is, of course, Julia) on the street.
His first reaction to her is real fear. He is sure that she has been sent to spy on him by the thought police. He imagines that her presence is proof that they are "on to" him.
When he sees her what he does is to consider killing her. He wonders if the piece of glass he is carrying will be heavy enough to do the job. In the end, of course, he figures that he wouldn't be strong enough to kill her easily, so he doesn't try.
Previous to Chapter 8, Winston already suspects the dark-haired girl of spying on him. So, when he sees her after he has been in the prole's shop and already feels uneasy, he suspects that she is following him so that she can report his suspicious behavior and actions to the Party. As he hurries down the street, he considers picking up an object and smashing in her brains, and when he returns to his dingy quarters, he thinks about committing suicide before she turns him in to the Party and they send someone to vaporize him.
In Chapter Eight of 1984, Winston takes a walk through a prole neighborhood and visits a pub and an antique shop. After chatting with the owner of the shop, Mr. Charrington, and purchasing a paperweight from the man, Winston departs. He spots the dark-haired girl from the fiction department on the street and becomes paranoid that she is following him.
His guttural impulse is to kill the girl by taking the paperweight he has bought or a cobblestone and crushing her head with it. His absolute terror stops him from doing so, and he recalls O'Brien's voice from his dream and what was said to him: "We shall meet in the place where there is no darkness." Winston feels certain that he will be outed soon as a thought-criminal and considers suicide to avoid the repercussions.