Dogecoin is an inflationary coin. While it may have a stable price and be very useful in micro-transaction, it is unlikely to attract speculative investors. So the price is not likely to take off.
Inflation is something we consider to be bad for a coin as there are ways in cryptoworld to avoid it. Nevetheless, the real money we all use most of our time is all inflationary and we seem to be okay with it. What is really good about doge is that it can not face a fork problem. And this is what may make it popular in the future in case bitcoin and ethereum suffer from a hard fork.
Oh, and you were saying that doge price is not likely to grow much but it is growing as we are talking. Almost +50% for the past 24 hours.