What a great opportunity for your family! Is it possible? Absolutely. Will it be easy or pleasant? Most likely, much of the time it will be an encumbrance. There are trade offs.
At 5, a hoomschooled child can learn everything they need to on the go. (I.e., the requirements are low. "Oooo, see those giraffes? How many are there? How many would there be if three more came to join them? What letter does 'giraffe' start with? Great! Can you print that letter for me?")
At 9, the demands are greater, and while you can read to your child on the go, do you want to? Will the child have a few (I'd say at least 3) hours a day of uninterrupted sit down and teach/learn time in addition to stuff you do on the go? Because if you want the 9 yo to go back to school into the same class as he was with before, he will need to master the same subject material to keep up. Homeschooled kids don't need to do homework at that age. But you'll need to find out the legalities (do you need to submit goals and objectives/lesson plans to the school district? Do you need to submit samples of his work? Or will a standardized test be adequate? Goals and objectives take time. Proff of mastery of the material may take time as well.)
Re: curriculum, in the US, schools are legally obligated to loan you all the materials they use for their regular attendees, but they do not need to provide you with the teacher's manuals (the answer book, the book that advises teaching approaches and related activities, etc.). So, you need to know everything that the child is learning (you learn with the child.)
Opinion: I would not pass up the opportunity to travel extensively for a year just for school, nor would I give the kids a year off. Homeschooling a 5 year old only takes patience. Homeschooling a 9 year old takes some time and effort, but even more, it takes a great deal of commitment. If you don't have it, your child will fall behind. That may or may not get you into legal trouble depending on your local laws.
I homeschooled my children with a curriculum mostly of my own devising. The year we built our house, the demands on my time between the builder and my job were such that I had to send them to school that year (but some were older than yours.) I can't imagine that travelling the world won't be demanding and tiring as well. Only you can decide how committed you are, what your priorities are, and know the legal requirements of your country/state/province/etc.
And try to talk to others who have done it.