I think you should be alarmed by now, she should have been sitting up alone around 6 months, maybe go see your doctor to make sure she had no developmental delays. good luck keep us posted.
I would definately go see your doctor. Our little guy does have developmental delays and he's making great gains but is 3 1/2 and we have him in therapy since he was 4 months old. He didn't sit alone until about 14 months. Is she making eye contact? You say she is grasping objects. and pulling up. How does she pull up to a stand without sitting? I'd definately get a dr. opinion and it may just take some physical therapy. I'd make sure she's hitting the other 8 month milestones as well and if not, push for therapy. The earlier the intervention, the better. I pushed when our little guy wasn't smiling at 2 months. I pushed and pushed and they finally believed me and by 4 months we had First Steps in doing Occupational Therapy, Speech/Feeding therapy (mainily feeding at 2 months), Physical therapy, vision therapy, and water therapy. It's amazing how far he's come! Good luck to you!