I am a US resident for 2010 and returned to India for good in July 2010. My daughter was born in India in Dec-2010.
In my US tax return for 2010 (filing as US resident alien), can I claim my daughter as dependent and get exemptions? What about child credit? She, as you would imagine, was not in US in 2010.

Please suggest.

If you do not have green card, you will file dual status tax return for 2010.
You can not claim your daughter except if she is US citizen