Dogecoin supports the Scrypt algorithm to be mined, just like Litecoin and Bitcoin. That means, that without an ASICs miner, you won't get much profit, even if you use a decent GPU.
First of all, forget CPU mining, you won't make any money from it. However, with a decent CPU and a reasonable coin to mine (XMR, ZCash and plenty more, just look around here) you can definitely make some profit. They feature other Algorithms, which are profitable by GPU mining, unlike the Scrypt algorithm.