I am a doula and a mama who liked to labor alone, and I would say that a doula might still be a help to you - you may not be in a mood/mental state to do a lot of talking with doctors, and how are you getting to the hospital if you have no support person and you are in late 1st stage labor? Walk? Taxi? I walked home from work for my 2nd birth, and that was actually a really lovely way to move into active labor, but I only live 3/4 of a mile from my job. A good doula will sit outside the door or in a corner, just being present to hold the space if that's what you want. I will say that I labored really well on my own, but during transition, I got really sort of stupid both times and didn't realize how far along I was, and a doula could spot that and alert the nurse (or NOT alert the nurse, if that's how you want to roll

). Also, even though I was alone (DH was inflating and filling the birth pool and my sister and DS1 were upstairs), I was glad to have my dog for company, and I was relieved when the midwives showed up because things were getting intense and I remember thinking right before they arrived and my body started pushing, "I don't know if I can do this until midnight."
I really think of a doula as a good insurance policy for a hospital birth - she will be there in case you realize that you need support, if you have an OB who turns out to be other than what you'd like, or the hospital is really busy and nobody is coming in to check on you and you can't vocalize your need for more water or find the call button in your labor daze. I would also say that having a doula might mean that since you are "taken care of," they come check on you less than if you were alone. A good nurse would be monitoring your fluid intake, making sure you pee, move, etc., but if the doula is there, she doesn't have to be as on it about some of that stuff.