Firstly, I'm sorry that your baby was sick....it's awful to see them feeling bad, and of course just makes the job of parenting that much harder. Perhaps it was coincidence or perhaps she did pick something up from the plane. It's impossible to know, really, and she's getting to the age where she's going to be more mobile and more exposed to germs no matter where she is. Like your's, my child was never sick until about 9 months of age. At that point, she had two mild colds and two minor diarrhea illness almost back to back. It's really just a function of the age they're at; they're moving around and curious, touching everything, trying to put everything in the mouth. But it does serve a purpose. The more every-day germs she's exposed to, the more ever-day illnesses she'll be immune to. It's natural vaccination, minus the painful shots and questionable ingredients!
As parents, it's tough to fight the urge to bleach and Purell everything in sight to prevent it...but really, she'll be missing out if she doesn't have this exposure to the world at this point in life. The thymus gland, which manufactures T-cells, is functioning at it's highest in the first two years of life if I'm remembering my old A&P lectures correctly. The t-cells her body makes now will remain with her throughout her life...so really it's no accident that the time which kids are getting grubby and most exposed to everything around them is also the time at which this important component of her immune system is forming. Kind of fascinating, really.
But none of that helps you when you have a sick kid, I know! In reality, the small and few studies done on transmission of airborne illnesses on planes show that it's really not as bad as we typically assume. This begs the question of why people often complain of getting sick after flying. My personal theory is that it's due to the near obscene dryness of the cabin air. The mucous in the mucous membranes in the nasal passages is really the first line of defense against airborne illnesses. It traps germs and allergens and dust and keeps it from entering the cells in the nasal passages. When the ambient air is so dry, this mucous dries up no matter how much water you drink. With that first line of defense gone, you're at greater risk of getting sick until that mucous has regenerated itself. As a flight attendant, I suffered from chronic sinusitis and allergies for a few years after starting my job, when I'd previously been rarely sick. I tried everything and complained to my GP and went to a couple of different ENT's and allergists. Nothing worked until I started thinking about how bone dry I'd often feel by the end of a long trip. Once I started regularly using a saline spray on board and using a neti pot after a long drying flight, I stopped getting sick. It's been years now since I've had a sinus or other upper respiratory problem, and that's the only thing I changed.
We fly with our 11 month old daughter often, and I always give her a spritz of saline if we're doing a long flight or have multiple legs in a day. She's never been sick after flying, and her two colds were during a long period on the ground. Perhaps it's a coincidence, perhaps not, but it doesn't hurt and certainly increases her comfort level in any case.
Sorry for the epic account, but that's my tip. Good luck in the future.