The word drone has many meanings to different people. If you mean a machine that can operate without a person on the machine that acts autonomously or by a remote controller, the answer to your question is many fold. Without answers of your own to define better what you are asking, there can be no one single answer.
1. Is this a flying machine, a stationary machine, or a machine that travels on the ground?
2. What is the means in which you want to move 10 gallons of water; i.e. a quart at a time, a gallon at a time, or the full 10 gallons at once?
3. How far do you want to move this water?
4. Assuming this is a flying machine, what configuration are you attempting to use; i.e. fixed wing, helicopter style or other?
5. Do you already have a machine in mind or in your possession that you want to use?
6. How much budget do you have for this project?
7. What is the goal of this machine, other than to carry 10 gallons of water; i.e. contest, curiosity, want to DIY, humanitarian?
8. Where will this be done, inside a building, outside in the open air?
9. If outside, what type of climate; i.e. frigid, moderate, equatorial, humid, hot?
10. Are there any other considerations that you have not mentioned?
This sounds like a cool project, but, without you further explaining and giving more requirements, you can't really expect to get much useful feedback here, as many of us are seasoned engineers and will expect you to be at least a small percentage as thorough in your requirements as we are in our projects. You seem to be a beginner that wants to learn, and the first thing to learn is to be very thorough in your requirements.
Hope this helps...