In my second viewing of The Force Awakens I thought I briefly saw a crude hand-made doll in Rey’s home that looked an awful lot like an X-Wing pilot. It appeared to have a helmet and an orange suit with white vest. Am I remembering correctly? She seems to know something about the rebellion so this could make sense.
Yes, the factbook 'The Force Awakens: The Visual Dictionary' specifically confirms that it's an "Alliance pilot doll".
There's also some good background on the doll to be found in the Junior novelisation
She wiped her mouth on her sleeve and took stock of her few possessions. They always brightened her day and reminded her that there was more to the galaxy than life on Jakku.
She had a doll she’d sewn together as a younger girl from the fabric of an orange flight suit. A canister stored rare flowers she’d plucked in the desert. Then there was the computer Rey had built out of scavenged parts.
Rey is depicted as being quite clearly smitten with the idea of The Rebellion so it's hardly a step of the imagination to think of her as finding their hunky pilots highly attractive in her younger days, or even envision herself as one of them.
Last, a banged-up pilot’s helmet she’d found in a Rebellion-era X-wing rested on a shelf. This was something she couldn’t toss away or redeem as salvage. It would be like dishonoring the pilot who had worn it.
This is also backed up by the Official Novelisation which describes it as a
... handmade doll fashioned from reclaimed orange flight suit material
It is laughable to assume that a 10 year girl living a life of deprivation would be weaving romantic fantasies about hunky X-Wing pilots and make the doll for that reason.
It is clearly because she dreams about BEING one - not everything related to a woman or girl character has to boil down to love interest for God's sake. Developmentally speaking, children fantasy play about what they idolize.
Additionally, while it is true she doesn't leave because she is waiting for her family, that doesn't mean she doesn't dream about life off of Jakku. She was left there to a life of virtual indentured slavery. Of course she wants to leave, and see if things would be better somewhere else. She just forces herself to stay because otherwise her family might never find her.
She wants to BE a pilot.