There are several definitions of doodlebug.
1) the larva of any of several insects
2) a small jet-propelled winged missile that carries a bomb
3) a small motor vehicle
Since she mentioned the war, I think "doodlebug" means
"a small jet-propelled winged missile that carries a bomb".
" contending" means "dealing with".
She was always on time, even when she had to try to not get hit and killed by bombs dropping from the sky as she went to school.