You've got lots of responses with very different viewpoints so let me chime in with my amalgam of viewpoints.
She doesn't "need" it at all, you are so right (and I totally disagree with the posters who say that she does - prior to the last 20-30 years where daycare has become the "norm": - most kids did not experienced forced socialization away from their Moms at all - and none until they had a sibling or went to school! Now because so many of us work and use daycare we try to flip it around and say kids "need it". bulls**t if you ask me).
That said, if you need to do it because you have your exam or for whatever reason (any reasons you have are valid), I think you can work it out. Many children who are fortunate enough to be with their parents when young get introduced to part time pre-school (usually 2 or 3 mornings/week) when they are 2 yrs 9 months old. SO, you are just doing it a little early. I totally disagree with the woman who said she won't adjust because she isn't there full time, that's ridiculous to me. How do all those part-time pre-schoolers adjust? Seriously, they do just fine, and so will yours. My daughter has a temperament that sounds similar to yours and had NEVER been left with a stranger (my Mom and a neighbor care for her) and we sent her to pre-school Tue/Thur mornings when she turned 3. It's just 9-11:45. She was not interested in going at all. The first day, I went and stayed there the whole time. I did not leave. But I tried to stay in the background so she could "play" etc. Remember, at this age they do not play with each other, they only play themselves while others are also playing. Parallel play. ANyway, the second time I also was prepared to stay the whole time, but at one point she seemed totally comfortable so I went over and gave her a kiss and told her I'd be back to pick her up in a little bit. No tears. Easy as pie. After that it was easy to drop her off. She needs about 5-10 minutes of transition time - she likes to show me what she is going to play with etc and then I leave. If I had just left her there on the first two days I believe the adjustment would have been a lot worse. SO, if you & the sitter are willing, maybe you can try to transition her a little like that.
Good luck - you sound like a great Mom and whatever you do I am sure it will work out.