Yes, you should stay on L1 for a bit.
Your pull-ups will improve quickly. You might want to try slowing your pace even more so that you have more time to recover between sets of pull-ups. You should then be able to get your chin over the bar more often.
Do you understand how the levels work?
If you are following the program as designed, you stay on a level until you successfully complete Day 3 in less than 5 minutes.
Best of luck!