Oh no, don't think you're doing anything wrong, we are all just figuring it out!
Do you think keep letting her have her after dinner nap, toilet then when she gets up and then when starts to do her tired behaviour, toilet & up to bed should be ok?
Definitely yes to this - so she's asleep 7ish til 9ish, then out for a wee. I would probably say straight to bed after that 9pm wee (maybe a bit of cuddling/calm chewing for about fifteen mins) and not out to toilet again as going outside can be so stimulating. You might find she can go longer between wees than you think but you don't really know til you try!
Her sleeping in the other room sounds really sensible too - it might even be that you shift into a lighter sleep around 5am and she can tell from your breathing and gets excited that it's time to get up. So moving her might really help. If anything, I would just say worry less about the toilet trips - they definitely can learn to go a much longer stretch overnight.
And sorry I misread the morning behaviour - a puppy full of energy between 5am and 7am sounds extremely testing (and takes me back to the newborn days of babies, shudder). I hope moving her helps with her settling back to sleep. They do get into routines, and it's so annoying if she thinks 5am = playtime, but I'm sure you will be able to shift her onto one that works better for you.