I am going to make a guess about Harley trying to play along with the bat family! In Suicide Squad she found out she has been working long enough to earn a full pardon, so technically she is free and has no warrants for her arrest at the moment! She is telling Batman that she is willing to give up that newfound freedom to do what he is incapable of, she can kill the joker for him and save his entire family from the constant reprisals!
When he said no, I kind of liked that she said outright, well if you fall, I am going to kill him no matter what you say!
But other than that I do agree that her voice does feel off! I guess it depends on which version of Harley we are getting, it could be that this suicide squad Harley is hardened personality wise after doing so many missions for Argus! She is not as silly as usual, and she seems like she is all business right now!
It doesn't even matter the whole event is inconsistent! I can't stand how Barbara, Jason, Dick, and Tim are all being written poorly through the event! At least Barbara isn't too bad, but Dick, Jason, and Tim, it's like the writers don't even know who these characters are at all! Stephanie and Cass are background and have no personality or input! I guess Kate came across ok in Detective, but even she was off a bit!