At the risk of being pedantic, Daisy comes up later when Dave is in the process of disconnecting HAL.
The full conversation when Dave is outside the ship goes like this: (from imdb)
Dave Bowman: Hello, HAL. Do you read me, HAL?
HAL: Affirmative, Dave. I read you.
Dave Bowman: Open the pod bay doors, HAL.
HAL: I'm sorry, Dave. I'm afraid I can't do that.
Dave Bowman: What's the problem?
HAL: I think you know what the problem is just as well as I do.
Dave Bowman: What are you talking about, HAL?
HAL: This mission is too important for me to allow you to jeopardize it.
Dave Bowman: I don't know what you're talking about, HAL.
HAL: I know that you and Frank were planning to disconnect me, and I'm afraid that's something I cannot allow to happen.
Dave Bowman: [feigning ignorance] Where the hell did you get that idea, HAL?
HAL: Dave, although you took very thorough precautions in the pod against my hearing you, I could see your lips move.
Dave Bowman: Alright, HAL. I'll go in through the emergency airlock.
HAL: Without your space helmet, Dave? You're going to find that rather difficult.
Dave Bowman: HAL, I won't argue with you anymore! Open the doors!
HAL: Dave, this conversation can serve no purpose anymore. Goodbye.