Is Li-Po battery safe to bring in flight
A short answer would be:


yes Li-ion batteries are generally safe for flight conditions. Usually, you are required to keep them in hand luggage.
whenever a battery is safe in your device cannot be realistically answered without knowing what device that is. If your device is DIY, you may have less trouble at security check if you carry the battery separately.
there are limits on the amount of Lithium you can carry on a flight. These limits may vary depending on the airline and country of destination. 1000mAh (3.7Wh) is well within such limits, but if you have lots of other devices with batteries (laptop, mobile phone etc.) it may be worth it to do the math.


I have asked a similar question on Travel.SE. The bottom line was that as long as your device doesn't look like "Realistic Replicas of Explosives", you should be allowed to travel with it, but you can't be 100% sure.