This depends on whether you intend on having the spool attatched to the reel.From my personal experience it will depend on the airline that you travel with & the location that you leave from. Here in Melbourne, they can be very difficult, meaning i have left here with spool attatched & been ok, but have also been in trouble in the same situation, to be safe just take the reel wih you & have your spool in your luggage.
PS: that is unless you can get a note from your mum saying that you will be good on your flight, they mght give you a leave pass.