The concept of felony murder is one that I didn't totally get at first either, so I understand where you are coming from.
Bear in mind that "murder" is not an act, it's a legal conclusion that the person convicted of it bears criminal responsibility for an unlawful death and must suffer the greatest consequences set for in the law for an unlawful death. If you see, with your own eyes, person A shoot person B you witness a homicide, it may be an act of murder but there's no way to actually know at the moment.
Murder, again, is a judgement of legal responsibility. If I contract with an assassin for the killing of someone and arrange for the killing to occur in the middle of the business day when I'm sitting in a meeting room with a dozen other people I'm still guilty of murder even though I never laid a hand on the victim, because my actions are what lead to the death of the victim.
What many talk about here is "premeditated" murder, which is a homicide that is planned in advance and carried out to completion past opportunities to stop the actions that result in the death of the victim. This is one of the most heinous acts that one can commit against their fellow man. For this we reserve the punishments of life in prison or execution.
What Casey is charged with is felony murder. This sounds redundant, as murder is a felony charge. What the charge actually means, however, is that a homicide resulted in close connection with ANOTHER felony. The homicide itself or any act intimately connected with the homicide, such as battery, cannot be the felony that qualifies.
Casey's qualifying felony (Florida has 16 possible) is aggravated child abuse. The State does not have to show that a specific act of child abuse resulted in Caylee's death, they need to show that Caylee was being abused as defined by the statute and ended up dead due, in some part, to a result of the abuse.
So if the State can show that Caylee was abused and the abuse lead to her death, then they have proven 1st degree murder. No premeditation is needed and does not have to be shown - she has not been charged that way. The State also does not have to show the precise mechanism of death, the precise time of death, and so forth. Most homicides occur with only the victim and perp present, to require the State to prove things that can only be known by the victim (who cannot speak) and the perp (who cannot be compelled to speak) would mean nobody could ever be convicted of murder if they do a little bit of planning. That's not how it works.