I'm assuming that you used fresh potting mix for your container? You shouldn't really need to fertilize that basil. Yes, it's a leafy annual, but you'll get better flavor out of the leaves if you let it grow a bit "lean." In fact, most of our culinary herbs like it lean.
If you're feeling like your basil needs a boost though, you might try some compost tea. Or a little topdressing of worm compost. Both have microorganisms that are beneficial to the soil, have some nutrients, and may deter some of the more nasty beasties.