Pwede kang mag-apply ng U.S. passport for her even without her citizenship certificate but remember that passports expire. Naturalization certificates don't. That's her document for life.
Here's a story about how one's failure to apply for an N-600 affected his life.
The fee is currently $460, non-refundable. Here are the requirements.
Speaking from my own experience using the USCIS L.A. district office, here are what you can expect when you file this form:
1. It will take forever before you'll get the certificate. All right, not really. But it will take about 6-8 months before you even get the interview letter.
2. When you file the N-600 with the payment, you won't get one of those official-looking receipts from the USCIS. You will get a small receipt that looks like it came from an adding machine. When I got this receipt I almost felt like I paid for a siopao instead of $255 - that was the fee a year ago. Now it's $460. Ang taas na ngayon, ano?
Tip: Pay with a personal check so that you have another evidence of payment (from your bank statement) that you could produce when needed.
3. The interview takes only a short time but when you get to the district office, be prepared to wait for about 1-2 hours to get your appointment called. Meaning, your appointment might say 9 a.m. but get comfy seats because you'll wait. Still, be there on time. After the interview, you will be asked to go to another room where you will wait some more before your child's citizenship certificate can be claimed.
4. The interview's purpose is to positively determine that all of the application details are legit and that the child is in fact yours and the same one on the application so if you have complete documents, your interview will be short (and hopefully, sweet, as ours was). No US history questions, like in the adult's citizenship interviews.
5. While you're waiting for the interview letter, use that 6-8 months of waiting time to make sure you have the originals or certified copies of your marriage contract, your child's birth cert, and of course, your naturalization certs.
6. Bring picture IDs (like passports) to the interview - your child's and yours. Bring all the other requirements as stated in the interview letter.
To periodically check on the status of your N-600 application, click here, then choose the district office when you reside. It will take you to another page where you can see which priority dates (the month of your application) are being currently processed. To test this, I entered Los Angeles, CA and I saw that the N-600 applications that they are processing now are those submitted back in July, 2007.
Call the USCIS at 800-375-5283 if you have more questions.