Fassbach said doctors were being especially cautious "now that she's going into the world".
Taylor, who has been in an incubator since she was born on October 24, was just 24cm long and weighed less than 283g.
"Even though she's only four pounds now, she's plump to me," Sonja Taylor, the baby's mother, said.
Baby Taylor has suffered respiratory and digestive problems, as well as a mild brain hemorrhage, but doctors believe there will not be any major long-term concerns.
Doctors say she is the world's smallest prematurely born baby and the first baby known to have survived after a gestation of fewer than 23 weeks.
Full-term births come after 37 to 40 weeks.