I think it depends entirely on what sort of child you have and what she wants to do.
I used to think it was essential for home educated kids to spend plenty of time in the company of groups of other children who are of similar age. But as other home ed parents have pointed out, adults don't always spend large amounts of time in groups with others of a similar age! In fact, in terms of social interaction adults have a wide range of "normal", from those who spend most of their time alone to those who are with their family but not other people to those who like to be in the thick of things for hours every day.
I've now met quite a large number of home educated children, from those who, like my older daughter, are out and about every single day to those who, like my younger daughter, almost never leave their parents and don't particularly want to go out to new places and chat very often. The main thing is that they should have access to social opportunities if they want them, and should have access to family or to solitude if that is what they want. I really think that by and large, you can tell what the child needs by looking at what the child wants. It's never going to be perfect, but if you are home educating in a large city I can't think you would find it too difficult to get a reasonable social balance for your daughter.
To answer your question directly, my older dd (an only child until she was 7) was so socially driven that I decided that my main job in parenting her was meeting that need. This resulted in many afternoons spent under an umbrella in the park while she played with whichever kid I had managed to borrow, and a lot of ferrying her around on the constant whirl of playdates, and cultivating the acquaintance of every parent who showed any interest in getting their children together with mine, and attending home ed groups which weren't entirely my cup of tea because (joy of joys) there were kids there. Now she is 12 it has got easy because she can organise her own social life and often transport herself to wherever she wants to go: we live in a city too, which is fantastic for giving older children independence.
Why not find the home ed groups near you and go along to reassure yourself that there will be easy contact with other families if and when you want it? People who have sociable kids and live more rurally often find ways to make things work too, but I should think it will be easier for you because of where you live.