I read a book when I was younger about a little girl who always had to be first and when that became true she was ate by an alligator.Can some one please tell me the name?

Not sure if this is what you're looking for, but there is a poem by Shel Silverstein (of course I can't think of the name off the top of my head) where there was a girl who always had to be first - and was rude about it - the ending has her needing to be first in line to what I believe was a cannibal/headhunter type character... my son has some of Shel Silversteins collections - I'll look through them and get you a title...

Okay - I found this off some website - it's called Ladies First:

Ladies First - Shel Silverstein (A Light in the Attic)

Pamela Purse yelled, "Ladies first,"
Pushing in front of the ice cream line.
Pamela Purse yelled, "Ladies first,"
Grabbing the ketchup at dinnertime.
Climbing on the morning bus
She'd shove right by all of us
And there'd be a tiff or a fight or a fuss
When Pamela Purse yelled, "Ladies first."

Pamela Purse screamed, "Ladies first,"
When we went off on our jungle trip.
Pamela Purse said her thirst was worse
And guzzled our water, every sip.
And when we got grabbed by that wild savage band,
Who tied us together and made us all stand
In a long line in front of the King of the land-
A cannibal known as Fry-'Em-Up Dan,
Who sat on his throne in a bib so grand
With a lick of his lips and a fork in his hand,
As he tried to decide who'd be first in the pan-
From back of the line, in that shrill voice of hers,
Pamela Purse yelled, "Ladies first."