I want to point out that I didn't mean that it's objectively more morally correct to kill the baby. Different people will give different answers, and there isn't a correct one, because morality isn't objective (isn't independent of the mind).
I agree that it might be flawed and inconsistent. That's because morality isn't objective. We use emotion to decide what, at a core level, we think is right and wrong. As Stormcrow discussed, there is no 'right' nor 'wrong' independent of our minds. The moral choices are only right because most people feel that they are. It's disconcerting, but I don't see another way to measure morality when one doesn't believe in anything divine.
I do tend to believe that what is moral to us is largely determined by the action that will bring the most amount of happiness, on average. This might resolve the issue here. The deaths of the ten people will bring more unhappiness than the death of the baby, so it is morally right to choose to kill the baby. And the doctor murdering his patient seems wrong to us because, as a general rule, doctors shouldn't do that. If they did, people would fear going to the doctor, which would result in more sickness and unhappiness. But there are exceptions even to this, I realise. I do see the problem.
But we aren't really dealing in reality. There's a purpose to the thought experiment. It's completely irrelevant that there might be loopholes in reality. Why does the fact that there are loopholes mean you can't even consider the hypothetical situation in which there aren't?
I'd like to add (I'm sure you know, but for other people's sakes, to clarify) that the dilemma isn't just "kill ten people or one person," it's "kill ten people who were going to die anyway or one person who wasn't." There is extra reluctance to kill the one person instead, because it involves taking a drastic measure, to go out of your way to murder someone who would have otherwise been entirely free from harm.
I can completely respect this opinion, because morality isn't objective. If someone genuinely values a cookie more than a person, then for them, the cookie is more valuable, even though I may disagree. I'd like to point out, however, that I'd completely understand if it were your baby who would be run over. I would kill 100 people to save a single person I cared about enough, I admit, even though I'd feel it was wrong on some level.
This will probably sound appalling to most people, and I know I likely stand alone here, but, to be honest, I value the lives of adults more than I do babies. Adults have entire lives and minds, while babies are not yet developed, not human enough. If I had a choice between killing a baby and an adult in his or her 20's or so, I would choose to kill the baby.
I want to bring up yet another of these scenarios. Imagine that you're driving along to save two people stranded somewhere twenty minutes away, about to die. For some reason, only you can save them. On your way there, you encounter a single person trapped in some way, calling for your help, who again only you can save. But, if you save the latter person, you know you won't have time to save the former two, and they will die.