You can actually carry pretty large LiPo batteries on a plane. You can have unlimited batteries up to 100 watt/hour, and for a 3S 11.1V lipo, that’s 9000mAH. You can additionally bring up to 2 batteries of up to 160 watt/hours, which would be about 14,5000mAH.
LiPo batteries are at the highest risk of fire when either charging or discharging. When they are simply sitting, they’re pretty safe. I plan on teaching a Lithium battery safety class soon, for anyone who wants to learn more about them.