The best way to get you're high score on doodle jump is to turn off all the volume so you don't get distracted and try to avoid shooting the monster and try to go around them. Also, you should avoid the cracks and go for all the springs.
On Doodle Jump you can get extra points by getting,
Propeller Hat: Gives you around 1200-1500 points. Jetpack: Gives you around 2800-3000 points. Rocket: Gives you around 6000-7000 points. (Only can be found in the space theme) Spring Shoes: Gives you around 500 points per jump.