The department is definitely called Employee Assistance. There used to be a woman there named Amal Bourey (sp?) who was quite helpful. They all seem sincere and sympathetic.
They will help you get your time off (and I think that's a wise and safe decision to do so, by the way) and they will help you get through it as well. It may eventually lead to some time with Corporate Psychology, particularly in assessing your fitness to return to flying. It's sort of a double-edged sword. You may want the time off without the apparent intrusion of (let's face it) a slightly impersonal department meddling in your very personal affairs but you can't have one without the other, not unless you lie about the reason for leave.
As for how much time...well the best cure, when the time is right, might be a return to what you do.
Stay strong and remember, time will absolutely soften the edges of this eventually.