She personally denies it quite vigorously. The implications are that she could be God if she wanted to, but doesn't think that's what the world needs. There also may or may not be something above her better deserving of the title, but he isn't exactly a conventional deity either, assuming that he's not just her creation, as well. Mind Screw, ahoy!
The premise of Kamichu!. The full title actually means "The Goddess, A Middle-School Girl"
Fukashigi Philia 's antagonist duo consists of a psychopathic modern-day slaver, and a girl with the power to make ALMOST anything she says come true instantly. This goes about as well as you can guess. Deconstructed when her reality-warping powers have unintended consequences (parents killed, brother traumatized, lots of bystander casualties), and when her partner screws her over by muting her, which de-powers her, even though she could have set up some powerful safeguards. It's implied that if she was more experienced with her powers and/or could alter human souls at the source, most of the plot wouldn't have happened.
Ivy (The Archive) in The Dresden Files contains the entire wealth of any knowledge that has ever been written down in any language throughout time... in the body of an 8-year old girl... who likes kitties.
Vin of Mistborn: The Original Trilogy is a 20-21-year-old, 5-foot-nothing girl who becomes 1/16 of a God explanation Eons ago, Adonalsium (this universe's God) broke into sixteen pieces known as the Shards of Adonalsium. Scadriel, the world of Mistborn, ended up with the Shards Ruin and Preservation.
In VALIS, Sophia, a two-year-old girl who may be the incarnation of divine wisdom.
Live Action TV
On Angel, Wolfram & Hart's conduit to the Senior Partners would sometimes manifest as a sweet little girl
God took the shape of an elementary-school girl a couple of times in Joan of Arcadia.
Supernatural: Lilith, arch-demon and de facto ruler of Hell while Satan is imprisoned, seems to prefer possessing little girls. While not God, she's at least as powerful as some small-g gods in the show.
The Groove Coverage song, "God Is a Girl" is just about that. The music video depicts the members of the music group as traveling show evangelists, convincing people into believing that an 11-year-old girl traveling with them is God.
It is implied in Demon The Fallen fluff that the Old World of DarknessGod is a girl. Since the Fallen are pretty much the only still-living beings who have actually seen God at the dawn of time, their word can be trusted.
Since the vast majority of the Fallen are still really, really pissed at God, don't put too much stock in their word.
God also has an evil sister named Oblivion, short for "The Grand Maw of Oblivion." Grand Maw wanted to create her own universe, and saying that she "failed" is not putting it strongly enough. Now she and her "offspring" spend their time gnawing underneath the afterlife until the end of the world.
Taken to the extreme in Ar tonelico series. Humans (and more) live in three gigantic towers that are also massive computers capable of potent magic. The Administrators of the towers are all little girls, especially Frelia.
However, they aren't Goddesses in the literal sense of the word due to actually getting their names from three Goddesses that lived millennia prior to them, and the fact that they are considered as such due to keeping the Towers, the last safe haven for life in Ar Ciel, functioning. However, a few of the personae of the Planet Ar Ciel (which are the actual creators and maintainers of said planet and all life on it) do fit the definition.
Elizabeth from BioShock Infinite effectively ascends to godhood the moment the Siphon is destroyed. While she is not almighty, since she is forced to operate within the limitations of constants and variables, by the end of the game, she can manipulate those variables and thus tweak the entire multiverse in any way she pleases. Exemplified by this exchange between her and the cynical, daredevil badass of a Player Character (which takes place even before her apotheosis):
Elizabeth: Booker, are you afraid of God? Booker: No. But I am afraid of you.
Hanyuu of Higurashi no Naku Koro ni is the true identity of Oyashiro-sama, and she takes the form of a young girl, appearing no older than Satoko or Rika.
Minus isn't really confirmed to be God in the comic - just a girl with limitless unexplained powers.
But she does create the Afterlife, and is shown to run it whenever she isn't busy having fun.
An old, discontinued webcomic, Acid Reflux, had a little deity girl get her own (used) universe as a present. Her name, of course, was "God". Much humor occurs when she's sucked into said universe, a sort of high fantasy pastiche.
In Bit F City, the most powerful Randomnian god, creater of a whole dimension, is a 6-year old. She also has the mentality of one.