I think it's absolutely wrong at such a young age. She is way too young to understand what is going on, or to have the ability to sooth herself to sleep. They develop those things later, but right now I think it would be really cruel to let her cry it out.
I didn't start sleep training Rowan in a way where she would cry by herself in her crib for a period of time until 7 plus months (I think it might have been 8 months). Now I will put her in the crib and she will cry while I put her there and while I'm walking out, and then for a couple of minutes after I close the door, then sleep. She sleeps so much better since I've allowed her to learn how to self sooth (now she won't fall asleep while I'm holding or rocking her anymore!). Babies that young don't have the ability to self-sooth yet. Their use to your warm belly, rocking them and holding them right. I know it's frustrating, young babies often don't sleep well, but I don't think leaving a baby that young to self-sooth is the right thing at all.
Rowan had colic, so she was a really bad sleeper. She spent practically all her awake time screaming, for four months. I would turn on the bath water for her to listen to, put her in her car seat in the bathroom, turn off the lights and rock the seat. It was the only way I could get her to sleep. Once she was asleep I would leave the room and the sound of the water in the background would keep her asleep. I obviously left the tub stopper out!