It is important when asked how long she lived with you, that you must put more than 6 months. This is only for babies born in the tax year. Once you do that, you should be able to claim her as well as get the daycare, EIC and child tax credit (if you qualify based on income). Congratulations on your newborn.
According to the IRS
-
To be your qualifying child for the earned income credit, a child
must live with you in the United States for more than half of the tax
year. You may treat a child who was born alive or died in 2016 as having
lived with you for more than half of 2016 if your main home was the
child’s main home for more than half of the time he or she was alive in
2016.
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The earned income credit requires that you provide a valid Social
Security number for your qualifying child. If you meet all of the other
requirements to claim this credit, and your child was born and died in
2014 and did not have a Social Security number, instead of an SSN, you
may enter "DIED" on line 2 of Schedule EIC (Form 1040A or 1040) (.pdf), Earned Income Credit, and attach a copy of the child's birth certificate or a hospital medical record showing a live birth.
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