Choosing technology is one of the problems, and Google docs are a good choice IMHO. But the real problem is how to manage the process, for example. split tasks.
My suggestion is to first make sure that the platform and all related technologies are resolved - as much as possible. Then make a detailed table of contents. A well-designed TOC will allow you to properly distribute tasks, rather than “pacing” each other's work. Since then, you are each "flesh" of its designated sections, and also look at each other's work.
In fact, each sub-section of the TOC becomes an atomic unit of work that can be assigned and maintained by an individual who is also responsible for these sections.
Good luck
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