Your 7 yr old sounds quite sensible, and you've obviously done some excellent groundwork about the rules. An hour sounds a little long, though - I find with mine that they're fine for a little while with TV, Wii, whatever, but then they get a little fidgety bored, which is where the trouble could start. How far you are from the house is another factor - I might go round to a neighbour for coffee for an hour, but not somewhere where it's 10mins or more to get back if they phone.
I know just what you mean about the tiresome begging in shops, but does she get pocket money? I started pocket money with my son around 7 and made sure it was a reasonable amount that could buy a comic or so, not just 20p, because then when he started the 'can I haaaaave it' whine in shops I could reply with 'I don't know, dear, can you? How much money do you have saved up in your wallet?'. Makes it not my problem then, and stops it being mean old mummy who said no.
So far, I've left my 10 yr old (then not quite 10) for two hours. Here in Switzerland the kids come home for lunch for two hours, but hubby and I wanted a day trip so I arranged for my 6yr old to go to a friend's and allowed my then 9 yr old come home, let himself in, eat his clingfilmed lunch, then go back to school again at 2. We were about an hour away but I had a neighbour on standby that he could go to if he got bored or lonely, and I rang him during lunch to check he was ok. He also sometimes comes home from school and lets himself in if I won't be back for half an hour for some reason or other.
My 6 yr old DD is left for 15 mins or so whilst I pop to the village shop. And on Monday she walked to school alone for the first time - she asked to do this in her best serious voice, 'because I know the way really well, Mummy, so won't get lost, and I'm very good about crossing the road'. Since she'd derailed the two main arguments (abduction isn't really in the public consciousness here and kids wander around alone all the time), I let her (it's about 5 mins walk, with one road with a pelican crossing). And even managed to not follow her all the way 50 yds behind :-)
This summer, I'm sure hubby and I will work up to putting the 6 yr old to bed and then leaving the 10 yr old in charge for an hour whilst we pop out into the village for a pint for an hour. I wouldn't put them both down to sleep and THEN go out, though - they would be very shocked to wake up and discover no-one was there.
And an added benefit to early independence is that they get themselves up at some godforsaken hour at the weekend, tip cereal in a bowl and watch cartoons until mid-morning without thinking to disturb you