Puppy Potty training tips to go outside

I just got Mochi October 20th. Her birthday is August 1st, 2025. She’s been using the bathroom inside on a pad but sometimes has accidents off it. So she does pretty well with them. When I take her outside, she doesn’t use the bathroom at all. She waits until we get back inside to use the bathroom. I was waiting for her third booster and rabies shot to start taking her outside. Should I take her out more often? She also doesn’t sleep in a crate and does her business in the middle of the night on the pad. Should I have her sleep in her crate and set an alarm to take her out at 3am-5am? Since that’s the time she usually wakes up.. she’s very smart & learns things quickly. She’s a cockapoo.