Some kids don't need as much rest as others. She not actually doing anything wrong. She awake and laying there in silence when so little even for a few mins is a long time. She's waking up and entertaining herself just not how you want her to.

Is it a big deal to get her up and let her play independently in the play room?

How long has she been asleep before she wake up, all fresh and raring to go?

I'd let her get up but understand that some carers insist on children stay in nap room for hours even if wide awake. If that not work for you, then another room is only option. Big ask to expect small child to stay in the crib and do so silently if they have napped and are recharged.