That is completely normal for that age. BUT my suggestion is to get your daughter a "buddy" - a dolly, a teddy bear, something soft/snuggly.
When our first was in a daycare center, we brought in a teddy bear one day, and they said they couldn't take it away from her because she'd scream - they'd "never seen a child take to a teddy bear that early and that quickly". A friend of ours gave our daughter a purple teddy bear at one point, and it hasn't left her side since.
Our youngest has a dolly and a "ming ming" (the duck from wonder pets, a show on noggin or something). She carries them around, and particularly wants them when we're getting ready to leave her at the sitter's in the morning.
Anyway - good luck!