The correct writing sample that uses pronouns correctly is:
"Jeannie is my best friend. She and I love playing with animals. We are starting a pet-sitting business together."
Jeannie is ours best friend. She and I love playing with animals. We are starting a pet-sitting business together.
Jeannie is my best friend. Her and I love playing with animals. We are starting a pet-sitting business together.
Jeannie is my best friend. She and I love playing with animals. We are starting a pet-sitting business together.
Jeannie is my best friend. She and I love playing with animals. Us are starting a pet-sitting business together.
The correct writing sample that uses pronouns correctly is:
"Jeannie is my best friend. She and I love playing with animals. We are starting a pet-sitting business together."