Communication through phone is an instantaneous form of contract where the parties communicate through phone and the acceptance or renovation of the offer is done immediately. the acceptance to offer becomes valid the moment the offeree assents to it. After proposal and acceptance, the contract becomes valid in binding. In the given case, you have mentioned that you contacted the seller and accepted to buy the puppy which shows that there was an existing contract and you have performed your part of the contract by paying the advance money.
You can sue the seller for breach of contract and file a suit in civil court for specific performance of a contract to force the other party to perform their part of the contract under Section 10 of Specific Relief Act, 1963.
Proceedings can also be started in a criminal court by filing a complaint before the police under Section 420 of IPC which deals with the provisions related to cheating but in case of this, it will have to be proved that the seller had the intention to cheat you and he did not intend to perform the contract from beginning itself.