In the novel, is the little girl Gatsby's child? Her name only appears once..........
There's no need to be unsure, Gatsby is not the father of Daisy's daughter in The Great Gatsby. The daughter has nothing to do with Gatsby.
The scene outlines Daisy's predicament--indeed, almost any female's predicament in 1920's America. Daisy tells Nick how crushed she was when she found out her baby was a girl. The girl would face the same situation Daisy and other women face: being a female in a patriarchal society. Daisy's defense mechanism is to flip flop and pronounce that she's happy her baby is a girl, and she hopes the girl is a little fool. Why? Because being a cute little fool is the only hope a female has of advancement. Her only chance is to marry someone wealthy. Daisy has lived most of her life without even being able to vote. She is stuck in a man's world.
Daisy tries to play off her sudden show of vulnerability and emotion to Nick by claiming she was only acting, by claiming she was just playing the cynic. Nick, an unreliable narrator, accepts this. But the situation Daisy's daughter faces is the same as the situation Daisy faced, and Daisy got out of it by marrying Tom. Daisy did what millions of women have done.
I do not know anything that would imply to us that Pammy is Gatsby's child.
We are told that Gatsby has not seen Daisy in quite some time so I do not think that there is any way that Pammy could be his kid.
I think that we can also see that Pammy is not his from the way in which her appearance is handled. It is, it seems, part of Gatsby and Daisy moving apart after they had seemed to be falling in love. If Pammy were his, I would think that seeing her would have drawn them together.