If I hit Karthus on a Baited Hook that used a Mixologist for fuel, do I get the double Deathknell?

No, you do not get the double Deathknell trigger in this scenario.

Karthus, Eternal must already be on the board at the moment a Deathknell trigger is created for his passive ability to apply.

Sequence of Resolution:

1. Baited Hook resolves: You kill your unit (the Mixologist).
2. The Deathknell trigger for the Mixologist becomes pending. It cannot enter the chain yet because Baited Hook is still resolving.
3. Baited Hook continues: You look at the top 5 cards and find Karthus, Eternal. You play him, and he becomes a pending item on the chain.
4. Baited Hook finishes resolving. Now, all pending items finalize in the order they were created:
   • First, the Deathknell trigger finalizes and enters the chain.
   • Second, Karthus finalizes and enters the board.
5. Because the Deathknell trigger was created and put on the chain before Karthus was on the board, his passive ability ("Your Deathknell effects trigger an additional time") does not see the event to double it.

Summary: Karthus needs to be on the board when the trigger happens, not just when it resolves. Since the Mixologist died while Karthus was still in your deck/pending, you only get the single, base Deathknell trigger.

Note: I could not fully verify this ruling against the retrieved rules.