We do the same thing with Izzy (she's 15 weeks old), I play her pretty hard from about 9:30 til about 11pm during this time I let her have a treat and water, then at 11 ish i put her in her litter box..she goes, then she goes right to bed...once in a while she will wake up around 3am but it's always cuz she has to pee..
after that she goes back to bed till around 6:30....