Why? Why jeopardise your friendship with her? It sounds like a date, and will look like a date to her if she hears about it. The secrecy will only make it worse.
If I was in the position of your friend I would most certainly think that you are backstabbing me. Firstly, you said that she was already getting paranoid. Surely you going out with him won't be a remedy for her many worries. Secondly, I know that if I went out with someone who had just told me they liked me, my boyfriend would NOT be happy. Thirdly, the fact that you and this guy are planning to hide this from her means that you know what you are doing is wrong. The reasonable thing to do in would hence be to refrain from going out with him. And lastly, you will jeaoporside your friendship. Are you sure you don't want anything more with this guy? Because it sounds like you are enjoying his attention and advances.