Maybe top heavy once the jar was empty, but with a full quart jar, I don't think it would be tippy at all. If you were nervous about it, 6 additional jars filled with water, placed around it would help 'secure it. a wrap of duct tape and it would be 100% stable. Or even just the jar holder out of your canning pot.

http://www.heirloom--seeds.com/canning_rack.jpg