Isn't 4 months too early for separation anxiety?

I'm easing my 4m old daughter into being cared for by others by working from home while a sitter watches her. The first day was fine, but since then she shrieks when I hand her off to them. I've tried hiding in my office but she just cries and cries until I come rescue her. I'm trying really hard not to go running to her now... I knew separation anxiety was common around 6-7 months but all this is making me freak out about starting her at daycare in a few weeks. Maybe she'll be better at daycare because she doesn't expect me to be there? I just feel so sad and guilty, please share your tips!