Short answer
No, this is not safe. Star fruit is toxic to dogs, containing high levels of oxalates that can cause kidney injury, which is especially risky for a puppy's small, developing system. Even a small amount can be dangerous. Call your vet or the ASPCA Animal Poison Control Center at 888-426-4435 right away for advice.
Star fruit — Food safety facts
Do not feed · Dogs · full breakdown on the linked food page
Carambola is very high in oxalates and has been linked to kidney injury in pets. Do not feed it.
The full verdict, portion guidance and serving notes are collected on the Star fruit food facts page.