How do the spiders work?

I had my old site www.fancyfeetsandals.com. I decided to switch to
www.fancyfeetjewelry.com and set fancyfeetsandals.com to redirect to
the new site. My search engine ranking is improving but it's under
the URL fancyfeetsandals.com not the new one. Granted, when someone
clicks on it, it does go to the current site. I just want to know why
the spiders are not picking up the new URL. I've tried typing 'fancy
feet jewelry' into the searches and I get the URL for the old site.
That tells me that the robots haven't picked up the new site yet. I
just thought maybe someone would have a few suggestions. Or maybe I
just need to be a little more patient and give it some time.

TIA
Laura
www.fancyfeetjewelry.com