I only have one cup of jasmine rice left, but plenty of basmati. Can I just mix them together in the rice cooker?
It shouldn't be a problem, since their cooking times are similar.
Since their cooking times are similar, I'm sure it would be no problem to mix them.
In my experience - maybe it depends on the rice cooker? - it's possible to cook two very different types of rice at once in a rice cooker.
For example, I've had no problems mixing brown and white rice in my rice cooker. I wash them separately, put brown rice on one side of the pot, white on the other, and then add water slowly so they don't get mixed around much. I put in as much water as I would if it were all brown rice and then cook as normally. The white rice comes out a little bit on the sticky side, but not to the point that it seems like gruel, and the brown rice is just right.