Selecting a random row in Django, quickly

I have a view which returns data associated with a randomly-chosen row from one of my models. I'm aware of order_by('?') and its performance problems, and I want to avoid using order_by('?') in my view.

Because the data in my model changes very rarely (if at all), I'm considering the approach of caching the entire model in memory between requests. I know how many records I'm dealing with, and I'm comfortable taking the memory hit. If the model does change somehow, I could regenerate the cache at that moment.

Is my strategy reasonable? If so, how do I implement it? If not, how can I quickly select a random row from a model that changes very rarely if at all?