Transitioning a co-sleeping baby to crib!!

I’ve been co-sleeping with my six month old for a few months now. She’s recently started spending the weekends at her dads house and he doesn’t co-sleep, and he’s apparently had a lot of issues getting her to fall asleep and stay asleep without having someone next to her. I’m about “co-sleeped out”, too 😂 she’s getting pretty big and I want my bed back, but I don’t even know where to begin!! How do I start? Do I just let her cry it out at first? She’s a light sleeper so anytime she falls asleep in my arms or her car seat, she wakes up when I try to move her and gets super pissed at me, so I’m not sure if letting her fall asleep on my bed and just moving her to her crib will work with her. Tips/advice from experience??