I know there are a lot of families who have their babies' ears pierced - we didn't in my family. But there are lots of adorable child-appropriate earrings so I'm not against it in any way. My DD had hers done as her 13th birthday present so it was a big deal when she became a teenager.
All that being said, I think a second piercing at this age is very out of the mainstream. Whether we like it or not people make judgements about others based on appearances. So the question is do you care "what people think" about your child's ear double piercings? Because some will think it's not age-appropriate and will wonder about your judgement. I recall a boy in my DD's 2nd grade class who had a gold loop earring. I hate to admit it - but I did wonder what kind of parents put a gold loop in a 7 yr old boy's ear? Ultimately, is it really important? No. In the long run it doesn't matter how many piercings a person has or where. It's all about their heart. (The young man who runs customer service ar our grocery store is a shocking sight to see, tall black lace up boots, crazy hair down his back, piercings and tattoos, a biker wallet with a chain, etc. BUT - he's the sweetest kid you'd ever meet. I think he's trying to make some kind of statement - or it's a grand test to deterine who is worthy of being his friend...)
To me it sounds like your daughter wants to be like her mom, she sees the second piercing as something grown up and she wants to be grown up like you. That's not a bad thing. IMHO I would tell her a second piercing is for grown-ups and when she gets to be a teenager you'll discuss when it's appropriate.
Also consider other things that she may want in the future that are more teen/adult appropriate and how you'll want to respond. Tattoos for example. My 15 yr old wants a tiny tattoo on her arm that is meaningful to her that represents a tough time she went through now that she feels she's out of it. I understand why she wants it, but I also think that she may regret it at some time so I am insisting she takes time in thinking about. When she's old enough to get the tatt without my authorization she'll have had more than 2 yrs to consider it. Even then I'm not sure an 18 yr old would make the right decision about something that she'd have to live with for another 60+ years...
Funny thing is I have a second piercing only in my right ear - and I almost never wear an earring in that hole as 2 earrings just feel uncomfortable to me.
These are the things in life that make us crazy. It's not the giant decisions like should we buy a house, should we get married, etc. It's the thousands of small decisions that we have to make over the weeks and months of our life. Good luck Mama!