i live with white rental carpets, so i get it.

i think at the stage your child is at
- rolling
- not sure if you know her poo=ing timetable or not, whether she even has one!
i would call it SUPERVISED nappy free time.
ONLY after she's just pooed (and been cleaned up) so you are pretty confident there won't be a repeat too soon.
Use a timer
Be on the mat with her

WHen my child started walking, for my own sanity, i gave her nappy free time on the changetable, let her play on that (lying down mostly, with tummy belt on), while i was standing right next to her, tidying the shelves right there. THen i would put a natural fibre FITTED nappy on her, and let her wear that without a cover. Let her be without a cover for 15 mins, then put a cover on.

when she was older, and the poos were very formed, i could have her at home walking around in fitted, no cover.

in warmer weather i gave her more nudie time in rooms with tiles (bathroom).

for toilet training, we used cloth trainers, - as using just knickers, meant poo escapes. Cloth trainers fit better around the leg holes, come in smaller sizing. Protect the car seat too. i coudln't risk losing the bond over the condition of the white carpet.

she has no outdoor space to play in either.