I'm with the others who say that you must be firm and consistent. Don't give in to her request for a baba. Don't argue, stay calm. Tell her there is no baba for her. Offer her the sippy cup. If she doesn't want it, then so be it. Put it away and walk away. She'll figure it out eventually.
As for how advanced she may or may not be, I don't know. But I'll tell you that even if she's a genius, it does not necessarily point to easy academic success. My eldest son seemed to be ahead of every child his age. Before age two he knew his alphabet, spoke in long sentences and even knew some sight words. By 3 he could read signs he saw when we were out driving. When he started kindergarten, he was reading at a 3rd grade level. Genius, right? LOL! That boy was the near-death experience for every teacher he ever had! Strong-willed and stubborn, but sweet and charismatic, as well. A month before his high school graduation, we received a fail notice for chemistry. He managed to pass in the nick of time, but it was just one more "Patrick moment" for all of us. His standardized testing was always off the chart, but he never was motivated by grades. He was very satisfied that he knew the material and saw no reason to prove it by doing homework. As a result, we refused to invest money in his college education unless he proved he could conform. He paid his own way through community college and aced his classes. He's now transferred to a state university and is still doing well, this time on our dime.
On the other hand, my youngest son never spoke a word until he was 3 years old. He could barely read even halfway through first grade. He was shy and withdrawn and we were sure there was something wrong with him. He was tested every way possible and he was completely fine. Turns out he's the natural born student now. Always in honors classes, fantastic grades, high SATs, Eagle Scout, scholarships.
Go figure. You never really know how they'll turn out. You just do your best to help them find their strengths and weakness and they almost always end up surprising us!