Based on the level of respect or formality, you can say "Thank you for taking good care of my little brother" in Korean in 3 ways:

• Informal: nae dongsaeng-eul jal dolboa jweoseo gomaweo (내 동생을 잘 돌봐줘서 고마워), nae dongsaeng-eul jal dolboa jweoseo gomapda (내 동생을 잘 돌봐줘서 고맙다)
• Formal: jae dongsaeng-eul jal dolboa jweoseo gomaweoyo (제 동생을 잘 돌봐줘서 고마워요), jae dongsaeng-eul jal dolboa jweoseo gomapseupnida (제 동생을 잘 돌봐줘서 고맙습니다), jae dongsaeng-eul jal dolboa jweoseo gamsa-hapnida (제 동생을 잘 돌봐줘서 감사합니다)
• Very Formal: jeo-eui dongsaeng-eul jal dolboa jusioseo gamsa-deuripnida (저의 동생을 잘 돌봐주셔서 감사드립니다)

- to thank: gomapda (고맙다), gamsa-hada (감사하다)
- you: neo-ege (너에게), ne-ge (네게), dangsin-ege (당신에게), dangsin-gge (당신께)
- to take care: dolboda (돌보다), bosalpida (보살피다)
- good: jotda (좋다), joeun (좋은)
- little brother: dongsaeng (동생)

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