Help me find this shoujo manga please

Looking for a manhwa. A poor orphan girl (around 12–14) lives on the streets with two brothers. The younger brother dies from illness, and the older brother sells her because she has a rare trait connected to the royal family (possibly eye color). The real princess recently died in a carriage accident, and an adult black-haired prince/noble buys the girl to replace her. The girl knows she’s a fake princess from the beginning and is trained to act like the dead princess. The crown prince is the princess’s younger brother and is bratty because everyone prefers his older half-brother. Later the fake princess saves the crown prince after they fall into a pit together.