I am a leader of a local charity group in the Richmond area and we're always looking to find ways to get our children involved. Sometimes, because of their age, children are not very welcome with certain organizations, due to the harsh realities faced by those in need, but there's really no reason they can't get involved.
The "hands on" part does not necessarily have to include actually visiting organizations and facilities to make an impact. I've cooked dinner at home (with my kids help) and delivered it to the medical respite for the homeless (they have no in-house kitchen). We've held warm clothing and basic needs (toiletries) drives to hand out to the homeless in Monroe Park (I do not recommend having kids younger than 10 to hand out items, it gets chaotic and they would need close supervision, but the kids LOVE gathering and organizing all the items to be passed out beforehand). We've also held a food drive for the Central VA Food Banks and the kids were helpful in getting all the food we collected moved and delivered.
A nursing home is a great place for children to volunteer.
As someone else mentioned, animal shelters also welcome volunteers, though I would suggest volunteering for Richmond Animal League if you choose to go that route (they get no federal funding, like the SPCA).
Veterans also appreciate having kids around, though you would have to check with the facility to see if they have age limits. You would want to prepare your child to see major injuries (amputees, etc.) if she's sensitive to that sort of thing, but kids tends to be very honest and have no problem asking "how did you lose your leg?", and vets tend to appreciate the candor.
Soup kitchens are usually good about letting kids help prepare and serve food, but again, that might be age dependent, depending on the facility.
You could also try calling a hospital (they usually have a hospitality center with a volunteer coordinator) to see if they can use young volunteers, though I think they prefer at least 13 years of age.
United Way has all kinds of volunteering opportunities to choose from.
You could also go to SoldiersAngels.org and adopt a soldier or send a care package, which is fun for kids.
I wish I could remember the name of the program, but I know there are some (Chesterfield County) schools that have a volunteering program just for kids. They do all sorts of projects, usually after school, making or collecting items to donate and my understanding is they get to make some of the deliveries themselves, so they can actually see where their work is going and the impact that it makes.
To be honest, at 7 years old, your daughter is going to be perceived as "too young" to effectively volunteer for most organizations, but anything that involves putting care packages together or gathering donations to deliver or even just cooking something together to deliver works fabulously for that age.
I could probably come up with some more ideas if my head wasn't aching right now, but I hope that helps some. And feel free to contact me if you'd like more information on anything I've mentioned.