There are plenty of portable dog bowls out there, and each design has its tradeoffs. The most popular format is probably the pop-up bowl, the design of which is sturdy and freestanding but takes up more space and weight.
The Rad Dog Pocket Bowl is targeted at runners, through hikers and others concerned with ounces and cubic inches. It stands on its own OK for food, but you'll probably need to hold it for any normal dog for watering. Not a huge deal if you're only wearing shorts and a fanny pack. If your dog is carrying his/her own gear, they will love you even more for saving their joints.
The Pocket Bowl has a narrower opening at the top than the bottom to give it some modest stability, although as the size of the snout and the enthusiasm of the animal increases the need for a helping hand does as well. We had no problems with leaking, although as is the nature of all ultralight gear it's not going to last forever. For its intended application the Rad Dog Pocket Bowl is hard to beat.