It IS possible to raise her as a vegetarian, and there's absolutely nothing wrong with that, provided you learn about nutrition and are vigilant about ensuring she's eating a balanced diet. Tyler doesn't eat meat, and he's stayed healthy with meat alternatives like legumes, nuts, seeds, and tofu. He just doesn't like meat at all, and DH and I rarely eat it, so I haven't bothered trying to get him to like it. I know there are other moms on here raising their kids without meat, so it's not uncommon.
That said, be aware that a vegan diet (no animal products at all) is generally not recommended for growing babies, according to the American Academy of Pediatrics. A natural foods store might have some dairy foods that you find more acceptable, but they can be more expensive.
I totally understand where you're coming from, though. I'm such a zealot about what Tyler eats (I'm learning to relax, but it's tough). If you're considering going meatless, I recommend the book Super Baby Food by Ruth Yaron. She advocates a meatless diet for babies, and I learned a lot about nutrition from that book. Good luck!