I don't find today's comic surprising. This is a talk Faye has needed to have with someone for a while now. You can only push this back and forth in your own head for so long before the thought itself becomes poison, which is where she has been since the Angus interview arc started. And really, there are only three people she could have gone to for this talk. Marten, obviously. Dora, who she couldn't go to right now. Once she's in a better place then yes. But talking with Dora would be it's own source of stress now. And finally Dr Corrine. Because you know, therapist. Of the three, she could probably help the most but is the least likely for Faye to go to without some external prompting, or after a revelation on her own. And of course, she gets paid to listen and help. Normally it's probably covered by her insurance, but the status of that is kind of up in the air now. Though I do think Friend Dora wouldn't mind keeping her on the insurance for that either.
Hanners is a good friend, and good to help out going to meetings and keeping busy so Faye doesn't drink. But she would actually probably be bad to have this talk to. Hanners has her own problems and a different way of dealing with life. The best advice she could give would probably be 'go talk to your therapist about this'. As a friend, sometimes that's a hard things to say when you want to help. But it can be the best thing you can tell them.
The last panel actually fills me with hope, not dread. If she was thinking of suicide then she probably would not have brought up her father. What she is feeling now is empathy and understanding. It is my thinking that a huge part of the reason why Faye has been in this holding pattern for years is because she never did really accept her father's suicide. She didn't understand it, or why he would do it. She's been stuck in feelings of loss, hurt, abandonment and confusion over his death. And has hid and drowned those feelings for years. Now that she's had a near death experience because of her drinking and depression she is starting to understand what it is that can drive someone to that final step. To feel like everything is hopeless, nothing will improve. That going on is just to hard to do, with no improvement in sight. And eventually, that feeling that there is only one way to stop the pain. She gets that now that she's been there herself. And since she's survived, thanks to her friend, she can hopefully start to come to terms with both her pain, and an understanding of her father's death. Once she can let that go, then her healing can truly begin.