It is possible but will depend very well on Elon Musk's influence. As long as he is committed to seeing doge pegged at $1 and the community is in support by bagging more, doge can get to a dollar. It is true that it doesn’t render any service but once it assures any investor of profits everyone will like it.
You know everytime elon trying to hype up doge some people lost money in flash pump and that means its gonna drive down the hype when he make a tweet regarding doge once more. I doubt it's gonna make doge goes beyond $1 not to mention every doge added to total supply every blocks mined, overtime making doge to $1 gonna take a lot of effort and that increases linearly.