Congratulations on your adventuresome family! It sounds like a wonderful opportunity for your daughter.
This is eminently doable, and you'll have surprisingly little trouble carrying this out. The simplest way is what I'll describe first. (May vary by state)
By law, every year every teacher must file official goals and objectives for the year on every subject taught, and often lesson plans as well.
When you know which elementary school years you want to travel, start looking for this information which is filed with the school district superintendent's office; the school principal will have copies as well, but I'd start with the district myself. (You might find a lot of this information for online. Search goals and objectives/expectations/reading lists/ etc.)
If you can get the same teachers' G&Os that will be teaching your daughter the rest of that year, that will help you to know exactly what the teachers want your daughter to learn in her absence.
Also, the school will lend you all the books and workbooks (except for teacher's answer keys and teaching/teacher's edition of the book) the kids will use during those years. You might have to pay a refundable fee for the books to guarantee their condition on return. Obviously, you pay for any books you might lose.
During the school year before you go, once you find out who her teacher will be for the year to come, make an appointment to meet with both teachers. Lightly peruse the textbooks, the workbooks, the reading list, and brush up on the G&Os/expectations before meeting with them. Tell them your plans, explain how you will cover all the required material you've read about, and sell them on the wonderful opportunities your daughter will have, especially what she can learn on her adventure - a second language, marine biology, exposure to a foreign culture - all of it.
Offer to give them a copy of your own G&Os (you can just discretely copy), and a sample of lesson plans (you only need one or two per subject for such a short absence) if they wants to see them. Ask their opinions of special projects your daughter can do based on your trip, and offer double the number of projects your daughter would be expected to do in school. Offer to do a skyped or taped special presentation on some incredible aspect of your trip. (This will also keep your daughter in the teachers' and students' minds.) This should buy you a lot of goodwill. They will probably have to meet with the principal, and you might too.
Then off you go, and make sure you do all of it and more. Keep all the worksheets, tests, etc. to turn over to the teachers on your return (graded, indexed by subject in a binder, of course, and with a summary of grades, etc.) You'll be schooling one student, which can be done in a fraction of the time it takes to teach an entire class because there's no waiting on other students to get their books out, to ask questions, to line up for recess, etc.
The harder way is to pull your daughter out of school and file to homeschool. If this is the route you take, you'll have to file a bit more paperwork with your school district. Search for the laws regarding homeschooling in California, e.g. here. Or, you can call your district supervisors office and ask them for guidelines. If you want to pay, there are often for-profit organizations which will do it for you. Mostly they prey on the insecurities of homeschooling parents, though. It's really not hard to do. You can gain a lot of information on forums with whose ideology you might disagree, but it's still useful (Don't join the HSLDA).
I would use the same tactics I discussed before - getting your daughter's teachers' G&Os/expectations - which will keep your daughter current and will allow her to return to class caught up or ahead - and use them to frame your own plans, and if California requires G&O's, etc., file them. You might have to cover the entire next year, though, but I'm not sure; that's why doing it through your daughter's school might be easier.
In any case, this is a great idea and a fantastic opportunity not to be missed! Enjoy the trip, and the preparations. Please let us know how it goes!