Pookie has depression and wants to die lol that's why she threw herself in the bullets way.
She doesn't care for him just yet all she cares for is where the music box would end up if he died. If she can die before getting the box I think she would be all joyous but she thinks the reason she can't die is because she doesn't have the box.
I also think so too since she also says in the recent chapters that it wouldn’t be good for him to die when he knows where he hid the music box she needs. Also in the beginning chapters, after failed attempts to commit suicide, she believes she is “cursed” to some extent to keep living until she returns that music box to her mother’s grave

pookie, isn't it too early being THAT CONCERNED to a man that don't even gaf about you? i thought she was depressed like desperately wanting to have that music box, and now she's all concerned about the duke being harmed, good lord.