Cooper's ale yeast makes a decent tasting cider, but (a) 1 gallon of juice in a 5 gallon carboy is way too much headspace--begging for trouble; (b) there will almost certainly be enough fermentation and sugar left after 10 days to create bombs if you bottle it.
I make cider/apfelwein in 1-gallon batches in the jug it comes in--why waste a container? Open it up, pitch the yeast and stick an airlock on it, and don't worry about your carboy.
After 2-4 weeks in the original jug then I rack to a one-gallon carboy, or even a PET water bottle if I don't have a glass carboy open, and allow another 4-6 weeks to finish clearing. Then treat it with Campden & potassium sorbate to make sure all fermentation is stopped. At that point you have something that you can bottle without an explosion and should only vaguely remind you of paint thinner. But it is drinkable at that point and will improve with age.
Do a search for the term "rhino farts" on this website--once your nose gets a whiff of apple juice that has only been fermenting for 10 days you'll have no problem letting it age for a few more weeks