This is Countdown, whose birthday is January 1, 2005.

There are three versions of this Beanie.
They have a poem that varies slightly from Beanie to Beanie. It goes like this:

As we count down to the New Year
Come on, join in, begin to cheer
We start it off with 10, 9, 8
2005 will sure be great!

or the last two lines read:

We're down to 7, 6, 5, and 4
2005 has good things in store!

or the last two lines read:

Nothing left but 3, 2, 1
2005 will be great fun!

Beanie Babies and Buddies