I would not worry about this at all OP.
Although, yes, grooming, eating disorders, drug dealers and kidnappers etc do exist... none of them would not be the first thing I thought of in this instance. She probably just wants to go for a run. Maybe she's seen a celeb doing the same online? Have a chat with her about it if you're worried about her anxiety by all means, but I don't think it's anything to stress about.
I have taught upper primary for years and at that age (9-11) they want their independence. Running up and down the street for 25 minutes is fine.
I have my own 11yr old DD and would not find it odd at all. She will be going to secondary school, on her own, in September. It's a walk to the bus stop, 40 mins bus ride and then another 10mins walk. Leaving around 7.15am in the morning, in inner city London. She will be fine.
However, in the 6 weeks holidays, you'd be lucky if you found any of us out of bed before 9am :-)
There's a tv show called 'sMothered' on TLC at 9pm tonight some posters on here should watch!