That's same case as mine.
After I received my passport, I applied a passport for my child who is Greencard and with me.
You apply her passport directly in State Department.
You have to present child's status as GC, Birth Certificate where your name is mentioned as a parent and your passport. That's it. You will get child's passport in a month or two.

micky_mouse
Thank you for the information.
Any idea if it is fine sending my kid back to Nepal(to stay with his Mother and grad parents) while my US citizen is in process and getting him back to USA before I sworn on citizenship.

deepocean,
I am not sure on that. My child was with me all the time. It was in 2012. I don't recommend to separate your child while you are waiting for your citizenship. Your situation is bit different because your spouse (or child's mother) is in Nepal but you are about to be a US citizen.
Consult a professionals.

Regards.

Thank you micky_mouse.
I do not think i will find any professional that would give me straight answer.
I will proceed with my research.

Your kid doesn’t need to be with you at the time of your oath. After you become the USC, your child will automatically become the USC when he is a GC holder living with you. Lets say you send your kid to Nepal at this time. Even if you bring your child to the US several months after you become the USC, your child will become a USC when he comes back and you can apply for child’s passport directly at that time. No need to do anything with USCIS unless you want to apply for child’s certificate of citizenship which is optional.

ark -
Thank you for the information.
Just wondering - What would be the purpose of child’s certificate of citizenship if a child holds a US passport.
Any suggestion what would be a valid evidence should USCIS asks to establish the child is/was living with me.
It's been a month since my child is with me here in USA. No day care and school she's been to so far. I am thinking of sending her back to Nepal to be with her grandparents.  So, just wanted to be sure that she will get US citizenship when she will be back to USA.

certificate of citizenship ( nagarikta) doesn’t expire ,
Passport expires
Always a good idea to take certificate of citizenship regardless of whether you possess a passport or not;

It depends on own preference, some people apply for it as it never expires, some people apply for it as they don’t want to apply for or renew passports unless required. If i were you, i wouldn’t waste ~$1200 on that.

Regarding evidence of your child living with you, you don’t need to worry about it. Your child, when in the US, is self understood to be living with you, unless it’s a divorce case.

U.S. Citizenship through Naturalization of a Parent

If you were born outside the United States and acquired U.S. citizenship through the naturalization of your parent(s), please submit the following with your passport application:

Your foreign birth certificate listing your parent(s)
Your parent(s)’ naturalization certificate
Evidence of your permanent residence status. Examples include:
Permanent Resident Card/Green Card
Foreign passport with the original I-551 visa entry stamp
Your parents' marriage certificate (if your parents were married when you legally entered the U.S. and before your 18th birthday)
Documentation of legal custody (if your parents were not married when you legally entered the U.S.)
Evidence of your legitimation (if your parents were not married at the time of your birth). Examples include:
Your parents' marriage certificate dated after your birth
Certified court order of legitimation

Thank you - ark and gandharba
Most probably I would send my kid back to Nepal while my naturalization is in process and get her back to USA to be with me before my Oath.
My ultimate intention is to have my child US citizenship automatically when I get one so, either she could stay here in USA or in Nepal as long as she wants.