In fact, most women find that they do not need any help at all in the early stages of labor. You may find you can go about your routine biz quite well between contractions; and during them, I will help you to understand good ways to relax through them, which should ease your discomfort. I actually made it all the way to 7cm without anybody around. The midwives kept telling me, on the phone, that I probably wasn't in hard labor because I was so calm! I believed them, and I don't regret that one bit!
You may find you really don't need your partner around at that point, either; but once they do arrive on the scene, many women find their loving support is enough for a good long while. It's a great arrangement when it works out that way, because you may not feel you need me until much later...when your partner is worn out and I am well-rested and ready! Fresh backup!
Yes, I am good with the occasional false alarm, and yes, I come to your home if you decide that is the course we will take at the time. I've even ridden in the back seat to births! That's okay.
There is so much variation in how things can work out, and it is impossible to give a really straight answer to the question of when your doula should arrive; but rest assured, we want to be there for you, and are looking forward to getting that (sometimes) late-night phone call!