I also have your dog and carpet issues. I lay down a towel or towels as the case may be.
If you use a steamer it won't take long to dry and you can block it in sections. There are some that aren't too expensive and have a large enough resevior to block, I got this one, http://www.walmart.com/catalog/produ...uct_id=4360372
. Yes it's OK to block wool with steam, it's the agitation that causes felting.