Congratulations on rescuing from a shelter! Would love to see pictures of your new addition.
Cats are instinctually nocturnal so kitty up playing at night is normal behaviour. Most cats adapt to their human schedules of sleeping through the night and active during the day but not all do.
Once kitty matures she'll settle into her own schedule which may or may not please you
Kitty may copy your 6 year old cats behaviour and sleep through the night
or have the odd "mad moment" during the night
She sounds perfectly normal to me
