I don't think this is too young to say "no" to a child. Sure, it doesn't hurt to give her an extra bath or an extra cookie, but it's also fine to start balancing your needs (and even desires) with hers. If you never "gave in" to her requests I think that would be too strict, but if you always drop everything to give her the bath, the cookie, or whatever, that's not going to foster a healthy attitude in the long run.
If she cries when she doesn't get her way, I would offer comfort, but not give in and give her what she wants if I've already said no. I know when my kids were babies, I always responded ASAP to their crying - I couldn't stand to hear them cry. It's hard to transition from that attitude (which I think is appropriate for a baby) to a toddler-appropriate attitude. Toddlers cry for different reasons than babies - if a toddler is crying because they didn't get their way or because they're frustrated that they can't do something, sometimes all you can do is to let them cry. Be there if she needs you, be loving, but learn not to overreact to crying.