You've said she's one. I'm assuming she's at the stage where she's either found her feet, or just finding them and wanders around the house (seemingly) for ages and possibly just started climbing! Won't sit still any longer, but wants to explore EVERYTHING -especially the things you don't want her to. She sounds normal to me. It's just a developmental thing. Kids want to see and experience everything.
My two don't watch much TV anymore, cause they're too busy running around most of the time. I don't see the point in leaving the TV on, if they're not watching it anyway. My daughter watched TV from baby-hood with BabyTV here in the UK (sounds similar to Sprout - 24hr programs, no commercials - pure heaven). If they start getting a bit fractious I chuck 'em outside and let them play in the garden. They love it rain or shine and it burns off they're energy.
If you really think your child is very hyper out of the norm, have you considered other aspects of day to day life? Possibly, something she's eating could be causing it, or could she be over tired? My son goes a bit doolally when he's over tired and runs around in circles (quite literally), as well as bumping into things and being gernally extra naughty. Also, with my daughter we noticed Fruit Shoots drinks used to make our daughter extra hyper and extra naughty when she'd drink them... It may be worth just paying a bit of extra attention to any changes of routines or when the changes happen to see if you can pinpoint it. Otherwise, it's probably just the normal extra energeticness of childhood.
Try not to worry on it too much. I know, easier said than done. Good luck!