Daughters 1st foods???

my daughter is 3 1/2 months old. i have been giving her deluted rice ceareal in her forumula once a day for a few weeks now. her dr said she could start having the babies 1st food and stuff at 4 months. well i am wondering if i could start them now. technically she is 15.5 weeks so she is like 4 months week wise but by the date she was born it wont be till the 22nd. so should i wait till the 22nd to start her on the food or is it okay now. i got her the babies 1st food gerber carrots.