The hardest part in shipping reptile is finding a shipping company who will ship reptiles. Most airlines may do it (Delta Airlines is one i know of. West Jet in Canada does as well but not completely sure about them now). Most couriers won't, though UPS may ship lizards. I think snakes is what they are very reluctant to ship. Some are very hard to ship reptiles through regardless if this is the first and likely only time you plan to ship reptiles through them.
Packaging is important. An insulated box should be used (insulated with the solid styrofoam sheets that are at least half an inch thick is best. Pink styrofoam insulation works great, as it isn't very expensive to buy and much easier to cut, without getting a whole bunch of little round bits of styrofoam all over the place). The insulation should be on all sides, including top and bottom. Depending on weather where you are shipping from to where it is going, you may need to use 48 hour heat packs or cool packs to ensure a comfortable temperature inside the box. The box should also be clearly marked with 'Live Harmless Reptile'. The species can also be marked though not necessary. (ie Inland Bearded Dragon, as well as scientific name).
The dragon should be placed inside a deli dish large enough for him to be comfortable but not able to move around alot. Basically, about one and half times the length of the body (snout to vent). The tail should curl comfortably and not at a sharp angle. The lid of the deli dish or small plastic container should be taped shut to prevent it accidently opening and letting your dragon get loose in the box. Ventilation holes need to be burned or drilled into the container as well. Papertowel or other soft lining inside works well to. It isn't necessary to put water in the container as this will most likely get spilled anyway. Make sure your dragon is well hydrated before shipping though I do not suggest feeding him the day you ship him. He won't have heat to properly digest anyway.
To pack up your dragon, I find it is best to do it the night before you ship. Wait till lights out and your dragon is asleep before putting him into the container. You can put him in the shipping box but don't close it up till you are ready to leave. THis pretty much leaves your dragon in a mini brumation (or just long sleep). Like a suddenly cool cloudy day in the wild. He will remain relatively inactive as he isn't warmed up as he would normally be under the basking spot. When ready to ship, box him up with heat pack etc and take him to the shipper the following day of putting him into the container.
I don't suggest shipping him twice in the same week, as shipping is stressful. It would be better to have him sent all in one trip. Overnight shipping is best, ensures less stress to the dragon and with a 48hour heat pack, he is ensures to have heat just in case unexpected delays force him to spend another night in the box.
If shipping across national borders, you definitely need to clearly mark the species on the box. There may be other regulations for shipping bearded dragons, maybe a CITES permit. Exporting dragons (or any wildlife) from Australia is prohibited, but captive bred bearded dragons are not a problem when born and bred in North American or Europe. TO know more about what you need to do to ship your bearded dragon outside of the US (or whatever country you are in) you will need to check the regulations for your given country and the import regulations for the country you are shipping in. ALso note some cities, states, provinces, etc. have prohibitions on what animals can be shipped or even owned as pets. Though the buyer should be aware of what regulations and laws exist in their home town/city/state/country etc. not all are or bother to check.
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PHLdyPayne