Absolutely fine for a 9 year old to walk to school alone one day a week! It's summer, it's light from 7am, school will ring you if she doesn't turn up. I've not heard of a school which doesn't allow year 6 children to walk alone, so you're only 6 months off what's considered the norm anyway. [As you've not indicated you've got concerns for her actual safety - would be a different answer if you'd said you did]
My only concern would be if she's used to the route and used to walking, but that's easily fixed by walking the route to school in prep (if grandparents are doing the rest of the day, then this may be something to ask them to do too).
Yes there are other things you could consider too (as per other posters, asking if a friends parents would have her for an hour before school, taxis, pocket money for older sibling to walk her to breakfast club, etc).
Call the school (that's offered you the job) back first thing in the morning, say you were very concerned about your own school drop offs, but have managed to work something out, so would love to take the job, if it's still an option!
I know several local parents here who have similar arrangements around 'I will take both girls to school if you drop Bessy off here an hour before school' and 'I'll bring both girls to ours for a bit, and drop them both off at Ballet'. If you're able to offer something in return this will probably be great for another parent who can't finish in time for after school club!