Does the block size issue also apply to Dogecoin?
It has been discussed before, but you're right that the problem isn't nearly as big. There are a couple of reasons for this:


Dogecoin has the same blocksize limit as Bitcoin, but it has ten times as many blocks, and therefore the limit is ten times higher.
As you say, there are fewer transactions on Dogecoin's network.
Hard forks are regarded differently within the Dogecoin community. For example, they recently altered their coin to remove the one hundred million coin cap. I don't think the Dogecoin devs would have any compunctions about raising the 1MB limit.