They're not allowed, for the pet's safety. Since figuring out the correct dosage is tough enough with animals, adding in the complications of cabin pressure, change in routine, etc, means that airlines refuse to fly sedated pets for fear that they'll react negatively to the sedative.
I know there's a hormonal spray for cats (Feliway) that's supposed to help calm them down (you would just spray it on the blanket that goes in the crate, so that it's environmental). There may be something similar for dogs.
First of all, there are no tranquilizers or sedatives that will last the full amount of time that your pet will be traveling (including time in the airport and at the animal reception center, maybe 15+ hours). And I want to reiterate that although most of the tranquilizers that we use are very safe (heck, I take a whopping dose of alprazolam - or xanax - when I fly with no ill-effects) since the animals cannot be monitored and altitude can change hemodynamics, it is really not a good idea to sedate them for air travel.
If it makes you feel better, one of my cats has HCM (hypertrophic cardiomyopathy) and has a heart murmur - I have no concerns at all about the effects of air travel on his heart disease (of course, your vet will need to evaluate your pets ability to get through travel safely). The biggest concern I have is the stress of the change in environment.
The absolute best possible thing you can do for your dog is to start now getting her used to the crate she will be traveling in - so that when she is in it, it is her "safe" place. Feed her in it, put soft wonderful blankets in it for her to sleep on, give her treats in it. Make it the BEST place EVER and that will do more to alleviate her stress than anything else you can do, honestly.
As Equestriannerd mentioned there are hormonal compounds that have been shown to relax/help alleviate stress. For dogs - there is something called "DAP" or Dog appeasing pheromone. It can be pricey, but you should be able to find a spray of this stuff at petsmart (or your vet might carry it). Spray it on blankets and in the carrier and this will help make it a happier place.
Good luck!!!