Have I failed Eileen the Crow's quest line?

I believe I missed her just outside of Oedon Chapel. After visiting the Hunter's Dream, she is not found there. Have I messed up her quest line?

I did speak to her in the sewers and I can still access the Oedon Tomb lamp. I have not opened any of the gates in Cathedral Ward nor have I fought Henryk as I need to talk to her first. I have not killed Darkbeast Pearl as I avoided (heeded the warning) about going to Old Yharnam.

Based on your comment, it seems like you haven't fulfilled the requirements for her to show up in outside of the Cathedral Ward just yet, which means you haven't failed her questline, fortunately. From the her wiki page:

Location 2: From the Cathedral Ward lamp: (1.) Head straight out, (2.) Immediately turn left tight when you exit the door, and you will see her standing next to the railing; (3.) If you have seen the Lesser Amygdala, she is standing in the same location. After exiting the doorway, turn left.

Notes:

• You must have opened two gates first: (A.) The large gate to the circular area, towards the Cathedral; and (2.) After going up the stairs, a short way, and turning right, you will have to pull a lever to open the smaller gate, leading back to the Cathedral Ward.
• Killing Darkbeast Paarl may cause her to disappear.
• Killing the Witch of Hemwick before speaking to her in Cathedral Ward will not affect her being in that location.

Thus, you need to open those gates first. Once you do that, make sure to speak with her to ensure that you don't miss out on the rest of her questline.

The doors are the maroon ones next to the (4) (you can only unlock it from within Cathedral Ward, not from the stairs leading up to it) and after the stairs leading right up from the plaza with the (1):