Don't forget that all 5 of them were hungry, and had been hiking for days. Since we are all sitting, well-fed and watered (and hopefully not in any immediate danger) in front of our computers, we have the luxury of unlimited foresight and a clear head. When one is in a dangerous situation, one tends to lose the ability to think absolutely clearly. I believe the desicion was much more on-the-spot than we imagine.
When I try to put myself in Littlefoot's case, I think of when I was 15, and got lost in a forest outside my old house. I had dozed off in a large tree, and woke up to find it about twilight. Remembering that dad said never to panic, I calmly slid out of the tree and thought about where to go. I thought: "Due to the Coriolis Effect, my body is tuned to walk counter-clockwise, since I live in the Northern Hemisphere. The sun is setting to my left, and in the morning I can see it from my bedroom window, which faces east. Therefore, east (and home) is to my right, and I should follow any paths that lead clockwise from my current position, since I want to retrace my path."
While it sounds like I had thought this through really well, in reality, I was cold, hungry and wanted to get home. I wasn't exactly sure what I was doing, and the logic was proably reall flawed, but I thought, "Screw it, I gotta do something." Also, I didn't have the luxury of double-checking my logic, and making sure I knew I was right: daylight was almost gone, and I needed to use it while I had it.
Also, to follow my unblazed clockwise direction, I strayed off the path and did some risky things I certainly wouldn't have tried during the day, in a safer stuation. However, once I had made my original desicion, I didn't think enough to even consider changing course. Evey move I made was calculated to shave as much time off of my journey as possible, regardless of the consquences if I misstep.
I wound up exiting the forest and finding myself downtown, which was petty far away from my house.
Anyway, the point is, Littlefoot and co. couldn't afford to think clearly, and weigh the possible solutions anymore than I could've 5 years ago. They needed to make a desicion and stick with it. Littlefoot conjured in his head a possibillity of a way to eliminate Sharptooth, and once it was fully formed, he implemented it. If the others had had any better ideas, they would've said them, but they obviously didn't. And then they fell into place behind him.
Also, if anyone says that Littlefoot didn't look tired or exhausted, trust me he probably was. One of the marks of a good leader is the ability to hide one's own exhaustion, and put on a brave face for the others in your party. since Littlefoot had shown in the past that he was going and willing to be their leader, he knew he'd have to act the part completely, to keep the others going.