Might be too late, but I have a few opinions on the matter.

First, the logo. IMO, avoid the square background in the logo. It detracts from what is actually going on in your logo. Any type of modern design is going to go the more abstract route, instead of making things look blocky. By have a square background in your logo you not only add to this blocky look, but you make it harder to modify the logo to use on different mediums, similar to what someone said before. Typically, you only want 2 or 3 colors in your logo. For example, what I would aim for is a white background (effectively no background) with a shape (dog, cat, pets, paw, etc) as a solid color and then put your name below, above, or beside it. The shape and name could be one solid color, or one for the shape and one for the name. Make sure you are 100% happy with your logo as you and your clientele will identify your brand with it forever.

For inspiration, here are some logos my graphic artist friend created. Notice how many of them are contained in a background.

http://www.luisjones.com/logos.html?sort=1

Also, to add a little bit to what Rob said about the website and keywords. He's right that the URL is important for SEO. The URL is the most powerful place you can have for targeting a keyword. You need to be careful about your meta keywords because sometimes doing too much can be more detrimental than beneficial. URL structure, page titles, meta description and keywords, along with keyword density in the content is what will get you better search results from search engines. When it comes to SEO, there are really an unlimited number of ways to do things, so if you want to talk more about it, I'm willing to help any way I can.