Juice can go in your carry-on (in the 1 quart bag) or in checked baggage.
Your battery is supposed to go only in your carry-on.
Be aware that many tank-style heads will leak e-juice due to the air-pressure difference, so don't fill your tanks before you leave! (And put tanks in their own baggie, so if they do leak it won't ruin other stuff!)
Have flown many times with vape gear, never a problem.
And, Congratulations!