Shall I apply now for citizenship now or is it better to wait until I deliver my baby so I don’t need to update my information?

Generally there is no advantage to delay the filing of a naturalization application beyond the earliest day of eligibility: for most Permanent Residents married to U.S. citizens, they may apply for naturalization as early as 90 days before the end of three years following grant of Permanent Resident status. In the event that your baby is born after you file the application but before your naturalization interview and examination, you simply should plan to identify your child at your interview and provide a copy of the child's birth certificate. The child's birth certificate, and even pre-natal medical records identifying your husband, can be helpful documentation to prove that you and your husband are still living in a bona fide marital relationship - strong and persuasive documentation of that type is needed for success when applying for naturalization earlier than five years following grant of Permanent Resident status. The naturalization application process often is significantly more complex than it may appear from reading the naturalization application form, its instructions, and material researched through the Internet. Inadequate supporting documentation or other errors can cause significant delays or even more harsh consequences. It would be wise to work with an immigration attorney for the naturalization application process.

You can apply as soon as you get eligible.