Your security deposit and your trade amount never left your wallet. Other then the fee all of those coins are still controlled by you. As long as you don’t lose your wallet or have the seed words and date, your money is safe.
You can always export your private keys in case of emergency.
There are no plans to re-introduce DOGE as far as I know, due to low trade activity, so you would be better off just doing your trade on the BTC network.