First, have you had your soil test done? its really cheap, if not free. Go to your county extension agent. You submit your test through them, and they give you a report that says how much nutrients you might need of which type, for your use. You may not even need to fertilize. But if you bag your grass, thats the same as mining the nutrients, so you will likely need to fertilize.
Second, check the label. Typically a seven day removal is recommended after fertilizing, but see what it says. You should either water it in or time your application with a nice rain. With appropriate care you shouldn't have any adverse effects.
I'm about to 2-4d (herbicide) our lawn, and I plan to keep the chickies of it for a while. But mine are in tractors, so its easier for me.
Good luck!