DD10 is an only and no amount of logic or reasoning ever satisfied on this topic.
Us: "If you had brothers or sisters you wouldn't get as much attention. You wouldn't be able to do as much fun stuff. We would have to split resources, time, attention, etc. Every kid with siblings wishes at some point they were an only child" etc, etc, etc.
DD: "So? What's your point?"
No cousins or neighborhood kids close in age either. When she was about 4 DD started to create imaginary friends. Lots and lots of imaginary friends. (She called them her "children") She was always very sociable and outgoing so different from your DD, though. At about age 7 or 8 she began to get annoyed by her friends' younger siblings having tantrums. That helped a bit. Now those younger siblings are older and DD considers them her friends every bit as much as the older ones, much to the chagrin of the older ones
DD is careful to include the younger siblings in playdates, birthday parties, etc. Again often to the chagrin of the older kids. Oddly enough she now tends to gravitate towards other only children when making new friends. We usually don't find out they are only children until later so I'm not sure how that dynamic works. She has several friends she is so close to that they refer to each other as "sisters" or "cousins" which is nice.
So I guess my advice is to let her spend time around other kids as much as she is comfortable. She WILL find her way on this one. A close friend or 2 with similar personality or interests will probably help.
Oh and when she was 5 we got a new dog and told DD he was "her new little brother." Surprisingly it helped. Anytime he got into mischief or damaged something of hers we said "Well you said you wanted a little brother. That's what they do."
