The American Dietetic Association (ADA) is the best place to begin your research into earning this online degree. They offer advice on accredited degrees in nutrition as well.
To begin your research on the ADA website (above), go to Advanced Degrees. Then choose Accredited or Non-Accredited, depending on which degree you are aiming for. Then, click on the box, Only Programs Offering Distance Education.
In the past, I included the names of the schools here, but because each person needs to follow their own degree path (either Accredited or Non-Accredited) and the schools often change the degrees they offer over the years, I have decided to give you the ADA site (above) to search.
In these programs you may be required to take a written and oral examination and/or a research internship as well as complete a dissertation. As with obtaining any doctoral degree, completing a dissertation online in nutrition will not be any easier, but in the end the dreams you aspire to achieve with this PhD will be well within your reach. You will truly have earned the title of "Nutritionist" with this challenging, yet rewarding degree.
Source: author's own experience in the Dietetic/Nutrition field