Now What?

I was watering the hanging flower baskets on my back porch just now.  When I poured a glass of water into the second basket a very upset dark eyed junco came flying out ... I looked in the basket and this is what I found ...

So ... this is in the dog's yard and baby birds + barking dogs = not good!  Does anyone have any ideas?  Can I move the nest?  If I move the whole basket out of the dog's area will mama find it?

Help!!

PS : The nest is lined with Carly's hair ... there's a lot of that floating around for the birds to use : )