Hey!
I have shown chickens in 4-H for four years, and am the proud owner of the best 4-H chicken in my state, not to mention Reserve Champion Showmanship at State! I tend to spend a lot of time pushing Poultry, so I'm really glad to hear that you're encouraging your daughter!
Transportation: Depending on the breed, transportation needs might be different. My LF Sumatras have long tails and are a little high-spirited, so they have to travel in dark, smooth rubber tubs (think Rubbermaid) to decrease stimulation and chances to damage their feathers. These tubs work great for all breeds, and can transport several bantam birds. However, they are expensive. With breeds that are not so flippin' finicky as longtails, cat/dog carriers with hay on the bottom (more disposable than towels) are great. Goodwill is awesome for these. Don't give them food while in travel, and only water if it's a really long trip. Actually, most judges recommend not to feed your birds until after they've looked at the bird, because this makes them more perky and active. I'M NOT SAYING TO STARVE YOUR BIRD. I'm saying, don't give them food for an hour or two.
Illness: 4-H shows all have health checks performed by experienced 4-Her's or occasionally experienced adults. This eliminates most problems, but at regional shows this is not the case. Actually, the biggest problem is often making sure that YOUR birds aren't carrying mites or lice- both are universal problems for chicken breeders. I recommend powdering the birds every month, more often when getting close to show. Our showbirds are separated in coops by breed and do not have interaction with the other birds. This is not strictly necessary, but it's nice. You can also use the "all in, all out" process, which basically means that if all your birds go to the same place, they've probably all been exposed to the same things and it won't be as much of a problem. QUARANTINE!!! 30 days is best before introducing birds back into a flock that does not all go to shows.
Pecking order: IF there are any problems, they will be solved fairly quickly. This can be helped with later stages of quarantine taking place near where they can see each other.
If she needs any help with showmanship, fitting for show, or anything, feel free to pm me. I have lots of worksheets and experience in sharing my knowledge ( my poultry demonstrations have gotten Champions at state and county).
Yikes. That was a lot of horn-tooting. But, I really want your daughter to do well and promote chickens and BYC!