Disguise it as cookie - the airport does not generally take your food items unless they are forbidden when entering or leaving the Country. Mix a small amount (10g) of your starter with about 3-4 times the amount of unbleached or whole grain flour. Once you can no longer incorporate the flour press it flat to form a cookie - you can even add raisins to the disguise if you want. Place it in a plastic bag and store it in your travel bag with your other snacks. If asked just tell them its a macrobiotic cookie, which is pretty close to the truth...
Once you arrive at your destination remove any raisins that you might have added and break the cookie into pieces in a bowl - add water and flour as you would when refreshing your starter. Let it ferment for 4 - 12 hours depending on how you normally use your starter - use or store as usual.
I usually make a counter starter occasionally from my refrigerated starter. The recipe was 10g starter, 10g water, 20g of flour usually whole wheat and rye. The end result will be something like this. Sorry I don't have a cookie picture. 