I second what PPs have said about trying to convince her that she is lucky being an only - I'd stop doing that. She knows how she feels, and for every negative scenario you put in front of her, she can probably find many examples of where the opposite is true.
Throughout the teenage years, her focus and source of fun will shift from you to her peers, and this should be encouraged, I think.
It's great that you organise big trips with friends in the holidays, but I'd make a conscious effort to encourage her to have her friends round at your house more, maybe have sleepovers - transform your house from the quiet 'just the two of us' house, to THE house where the action is, and where the fun happens.
Perhaps only then, will it seem that being an only child has it's advantages, because you probably have the space and the time to have a bit of an open house policy.
Maybe don't tell her what the advantages are, but take positive steps to turn things around, and then she can work out for herself that in some respects, being an only can be great.
For context, I'm not an only, and am several years younger than my sister. Growing up we had nothing in common, and she resented and bullied me for the duration of my childhood. She was cruel at times. We aren't close, she drains me as an adult.
Rather than make me want an only child, it made me want a big, happy, close family, and be determined to nurture the relationships that my DCs have with each other. I never wished that I didn't have a sister, I wished that I had more siblings, because then the chances of one of them being kind would be greater.
My DCs are incredibly close, and actively choose to spend time together, as a big group, and then pairing up to do things together, but they also get quiet time when they need it, and they haven't missed out on anything. They have what they need, but rarely more than they need, and that's an important lesson.
The eldest has moved out and is now married with a child. The others adore their nephew, and vice versa, and they spend as much time together as they can.
This is what I saw and wanted for my future self growing up - big families seemed such fun, and I craved that. I completely understand where your daughter is coming from.
Their lives haven't been all roses, we are still feeling from me leaving their abusive father, but throughout the trauma, they haven't just had me, they've had each other, thank God. They are quite PollyAnna-ish (good phrase from PP) in nature, thankfully.