Doge coin is on a large number of both big and small exchanges so binance is not any important factor for it. Billionaires like Elon Musk, Mark Cuban and other celebrities are driving its rise in popularity.
Exchange is just a one factor for the success of every project so Binance also help DOGE succeed but on its recent peak its just because of Elon Musk hype and that’s too risky to follow that hype if you’re too emotional. Right now, after reaching its peak, its down almost 50% so this is how volatile DOGE is so you have to deal with it carefully.