Rabi'a -al- Adawiyya, often called Rabia Basri, since she was from Basra, Iraq was probably the first female saint of Islam. She lived a few decades after the passing of Prophet Muhammad. She was firmly against rituals, and believed in cleansing oneself of egoistic thought. She was also a vegetarian.

Said she:

I carry a torch in one hand
And a bucket of water in the other:
With these things I am going to set fire to Heaven
And put out the flames of Hell
So that voyagers to God can rip the veils
And see the real goal.

She was very Meera-like in her absolute love for the creator.

O my Lord,
if I worship you
from fear of hell, burn me in hell.
If I worship you
from hope of Paradise, bar me from its gates.
But if I worship you
for yourself alone, grant me then the beauty of your Face.

Also see 1, 2 and 3. There's also a book on her on Amazon, and a much cheaper version in Overstock.

Incidentally, while digging up info on Rabia Basri, I came across a site for Muslim vegetarians.