Dna encodes the information necessary to produce the proteins needed by your body. while this is true for humans, is it the case for other organisms?

Yes, it's true for all living organisms. 

All animals/plants are made up of cells, and DNA contains the info/data for these cells to develop properly.

If you think about evolution more broadly, all living organisms evolved from single-cell organisms, so it would make sense that DNA is an important part of all of their growth/development.

Ithink the answer is nuclear membrane