Dear V.,
Most children will get sick for the first 6-12 months when they enter either daycare or school. The good news for daycare children is that most likely they will not be sick when they enter kindergarten.
Keep in mind that going to daycare part-time is not going to reduce the illnesses she is exposed to when at daycare.
When my 3 1/2 year old was 6 months old, I went back to work 4 days per week. I was off on Wednesdays and stayed home with him. That was a good situation for me since it meant I never had to deal with more than 2 days of getting him up and to daycare and commuting! When he turned 18 months, I left that job and began working 3 days per week, Monday, Wed., Friday. Since then my son has been in daycare on those days. It was harder when he was younger, I honestly think that he didn't understand the routine. Now that he has a good grasp on time and knows the days of the week, he is pretty well adjusted. I love having the 2 days off per week to stay home with him - and NOT commute!
If you have a job, then just be happy that you have one! It is a real blessing in this economy. Next year, your daughter would probably go to VPK anyways, and daycare is giving her a chance to adjust to school. If you are confident about your daycare, and your daughter seems happy there, then just know that you have a rough patch to get through and then you'll have a child that rarely gets sick! My son got everything from "daycare crud" (constant runny nose) to ear infections, to bronchitis, etc in the first year after he started daycare. He hasn't been sick now in almost a year (since an airplane flight from CA to FL last Christmas).
Best wishes,
C.