Dogecoin is merge-mined with LTC using scrypt (algorithm). Note most coins are based on different algo!
(algo name - coins based on this algo)
sha256 - BTC, BCH..
scypt - LTC,DOGE ..
ethash- ETH ..
equihash- ZEC,KMD ..
...
GPU's can mine almost every algo but those popular (scrypt,sha256 ..) are mined MUCH MORE effectively by ASICs and you'll just waste energy.
GPU's have different rate for each algo. rx580 can do 30MH mining ethash, but only 13 Mh/s mining KawPow ... (note power consumption also changes )
Try checking
whattomine.com and similar sites to estimate ernings.
Much better is to mine ethash (ETH) and sell mined coins.
Alternatively you can mine on pool which offers payout in various coins.
Check
prohashing.com - they have nice overview (algos/coins/profitability), you can mine ETH and select DOGE as payout.
As of earnings for your rx580 (my guestimate): Minig 0.0009 ETH ($3), selling for doge to get 5-6 DOGE daily.