Been taking Zyprexa (olanzapine) 2.5mg for about a month. Just gone down to 1.25mg. Doctor said I can stop them now, will I get withdrawals from stopping?

Unlikely. Your doctor is tapering you slowly, which is cautious and sound. Your dose is very small. You should be fine. If you feel any malaise or not quite right, check with prescribing doctor. Hope all goes well for you off this med.
Likely, Maybe Mild. You have been on 2.5mg/day for a month. Now you are down to 1.25mg/day. Since you haven't been on Olanzapine for too long, eventually stopping altogether may only produce mild withdrawal symptoms such as anxiety, restlessness, insomnia, mood dysregulation, and these symptoms may last for 1-2 weeks. Everyone is different though so stay in contact with your prescribing (or unprescribing) provider. .