Meaning of "duck"

This is an extract from the subtitles of a television series (Bones) in which Brennan have a talk with Booth:

Booth: The director will create a special unit. If I line my ducks up, I can head it up.

Brennan: I think I could be a duck.

Booth: No, we stick to the book. Cops in the street, squints in the lab.

Brennan: In this case, the Jeffersonian will issue a press release.

Booth: You do that, I'm a dead duck

I understand the meaning of the whole dialogue in principle, but the multiple use of the word duck in different ways makes me confused.

Because Brennan said "I could be a duck" I thought that "line my ducks up" means to line up a team. But this makes no sense to me at all. In the TV series, there are always the same people involved in investigations.

According to these idioms "get your ducks in a row" means "to organize things well". This makes sense. But now Brennan's answer is nonsensical.

Which meaning has duck in the first sentence by Brennan?

^{Note: I understand the latter duck (dead duck); it is explained as "someone or something that is certain to die or fail" and, likely, just used to complete this wordplay.}

Answer

This is all wordplay based on two idioms, both of which you mentioned:

ducks in a row or ducks in a line — plan every detail out

sitting duck or dead duck — being in a position with no desirable outcome; usually involving someone shooting or killing you

Booth's initial, "If I line my ducks up..." implies that if he plans every detail out just right he can lead the special unit. Brennan's offer of being a "duck" is an offer to help Booth out — she can be one of the details in Booth's planning. This is the answer to your question, "Which meaning has duck in the first sentence by Brennan?"

The next two lines set up Booth's final statement which switches to the "dead duck" idiom. The wordplay here is simply banking off of the earlier use of a separate duck idiom. The two uses are not specifically related other than they both refer to ducks.