Awwwww! I don't know if she's part Savannah, but she has a "squeaky flywheel" purr! I have heard other cats with that kind of purr who were just "moggies" - you know - mutt cats. She is also giving you love blinkies!
She is beautiful. Her fur looks ticked... but she's definitely a tabby. Besides, without papers, there is really no way to know.
Is that an EMU blanket on your bed? Are you a student there? My sis teaches there.
ETA: my guess is that she is a loving, loud-purring domestic shorthair.
BTW - Savannahs are big muscular cats with the arrowhead- rosette spots on them like their wild ancestors.