Hi @Kentishgirl,
Welcome to the Dyson Community, and congratulations on your new Dyson Airstrait straightener!
There shouldn’t be any problem with you storing your straightener in either your cabin or hold luggage. You may want to double-check with your airline for peace of mind, but as it’s mains-powered and doesn’t include a battery, we wouldn’t expect there to be an issue here.
Depending on your travel destination, please keep in mind that your Dyson Airstrait straightener is engineered to run on the voltage of the country you purchased it in. It won't work at different voltages, and we’d advise against using it with an adaptor - we can’t guarantee this won’t cause damage to your machine. You can find some more information on this here:
Hope this helps, but let us know if you have any other questions!