Based on the level of respect or formality, you can say "I'm the only daughter in the family" in Korean in 3 ways:

• Informal: na-neun munamdoknyeo-ya (나는 무남독녀야)
• Formal: jeo-neun munamdoknyeo-yeyo (저는 무남독녀예요), jeo-neun munamdoknyeo-ipnida (저는 무남독녀입니다)
• Very Formal: jeo-neun munamdoknyeo-ipnida (저는 무남독녀입니다)

- I: na-neun (나는), jeo-neun (저는)
- the only daughter in the family: munamdoknyeo (무남독녀)

Please refer to How to pronounce Korean Alphabet for the English pronunciation in this answer.