Good question! While the name of the coin has the word "Doge" because its fun and meme-worthy, the underlying technology is entirely different.
While Doge Coin, Bitcoin and current Ethereum network use proof-of-work consensus, Doge Protocol will use proof-of-stake consensus.
That, coupled with the quantum-resistance and sharding, will provide a robust blockchain technology.

Please see the Quantum Resistance Whitepaper for details: https://dogeprotocol.org/whitepapers/Doge-Protocol-Blockchain-Quantum-Resistance-Whitepaper.pdf