If it is not your key, then it is not your coin on blockchain, it is not your key, it is GitBTC key and Doge withdrawal was disabled. I have noticed if a coin is having thisnjssue on some exchanges, the coin price may not be correct. The deposit should have been disabled also, but anything stupid can come up from a centralized body like this type.
All I can say if to try to want convert it to USDT, I think the value of USDT it will be converted to will be displayed, if not displayed, do not take the risk to convert. If it displayed and it is indicating the actual price you are expecting, then you can trade the doge for USDT and then send it out of the exchange to convert it to any coin of your choice on a reputed exchange you sent it to.
HitBTC is one of the exchanges that is unrecommendable, they usually freeze customer's accounts and also have exorbitant transaction fee which is very high even for altcoins. So far you will still convert back to doge, you can look for exchange that support digibyte and doge, then you can convert it to digibyte on the HitBTC and then to doge on another exchange you transfer digibyte to. Digibyte fee is still less on the exchange if compared to other altcoins.
I ha e used HitBTC before until I joined this forum to know how the exchange is not worth to be used.
Make sure know the amount it will be converted in USD and relate it to your doge balance before converting it, if HitBTC wants to cheat you, do not convert, you will have no option than to wait until the withdrawal is working good again.