If you're flying with the pup in the cabin with you,
you can avoid "accidents" by avoiding a meal
before the flight, depending on what time of
day it is. If it's a two hour morning flight, skip
breakfast and feed the dog when you get
home, or get up super early and feed it to give
it time to get rid of everything

I hesitate to say
hold back water, because even people get dehydrated
on a flight, but remember that the dog has to be
in the crate all while you're checking in (they'll probably
remove him at the security checkpoint to go through
the crate). Don't know if you're technically allowed to
hold the pup in your arms in the waiting area -- I've
seen it done. Consider the time of day and make plans
accordingly. Don't let anybody talk you into drugging
the dog.
If you decide to drive, you can carry a tarp cut up into
large squares and a bunch of newspapers. When you
get to a rest area, put down a piece of tarp and papers.
Let the dog do its business, then fold them all up
and throw away. With a tiny puppy I'd move
off to one side but still do it on the parkinglot,
not grass where other dogs will be walking. Try not to do
it near picnic benches or anywhere people might be grossed
out. Most people will find a puppy cute, though!
Having the precut tarp will keep you from having to
carry a soiled tarp along on the ride. It also looks a lot
more considerate to other passersby than just plopping the
dog on newspaper on the ground. Your breeder could
even begin this process for you at her house so the
pup wouldn't be spooked by it.