At this very moment, there are no known exchanges you can buy BabyDoge ETH (BABYDOGE) on.
But because BabyDoge ETH (BABYDOGE) is an ERC20 token, you can use a decentralized exchange like Uniswap if the pair has any liquidity added to trade.
You can get the contract address of BabyDoge ETH (BABYDOGE) here.