I fly with my dog in-cabin cross-country about twice a year and she’s always been a great flyer - I do give her Benadryl (1mg/lb) p.o. about 15-20 min before boarding to promote snoozing.
She remains in her carrier in-flight, though I will open the top so she can stick her head out. In the airport, I take every opportunity to keep her out of her crate - I’ll find a quiet area without people around, take her out on a short leash, and we’ll hang out there together, her with something to chew on, until we need to head to the gate. Dogs are supposed to remain in-carrier in airports, but as long as you don’t flaunt that you have your dog out and stay out of everyone’s way, no one should bother you.
dogjaunt.com is a great resource for flying with small dogs, and lots of great suggestions on carrier choices as well. I have a large small dog - we toe the line for in-cabin size, she’s 15" at the shoulders and 18lbs but she’s black and very streamlined, so I haven’t had any issues. That being said, she’s heavy enough that I use a rolling bag that allows her to sit up when it’s being rolled, but when I lay it flat put under the seat, she has lots of lying-down room. I was also meticulous about training her to go willingly into her bag - the dog will need to be taken out of the bag through security and the last thing I wanted was to call attention to my large-ish dog trying to shove her back in the carrier after security.
My dog is also a high-energy nervous sort that loves to bark, and I’ve never had a problem with her at all flying - she sleeps the whole flight and doesn’t make a peep. I do exercise the hell out of her pre-flight though
You’ll be fine! Save lots of time over driving!