10 years or 20 years, it will not happen. 
First meme coin? Dogecoin ETF? Don't daydream large institutions will not make an ETF out of a meme coin. You already said that the coin doesn't any use case at all so why do you think that these institutions will make an ETF out of it?
Also, take note that DOGE is inflationary and yearly, 5 Billion new DOGE coins are being mined. That would affect the price of DOGE because of the increased supply, and if the demand isn't increasing, DOGE even at 1$ would be almost impossible to happen.
In short, it will not happen. I know that everything is possible in crypto, but at least let's be realistic sometimes.
I'm not sure about this, but I believe that BTC can reach $1M USD. However, it's not clear how much purchasing power $1M USD will have at that time. BTC may not increase in price, but fiat may simply depreciate against BTC. Similarly, DOGE could reach $10 USD in the future, but $10 USD may not be enough to buy food like it is today.
Currently, 1 DOGE = $0.17 USD and DOGE's market cap is ~$24B USD. If DOGE reaches $10 USD, we could see its market cap reach $1.5T USD. Of course, this is unlikely to happen in this current uptrend, but it could be possible in the future, if DOGE becomes a global currency. I'm not a dreamer, and I don't have DOGE in my portfolio, but I think DOGE is one of the tokens that has the potential to be widely used and survive in the long term.