if I do healthydogcareonline.com/blog can i still get good traffic or should i buy my blog its own domain?
You can still get very good traffic to your blog this way. I get good traffic on sites two and three directories deep, so that's not an issue. Just make sure you use some type of SEO plugin for your blog to rewrite the URL's and also to optimize the title and meta tags. Keep your blog posts focused on the topic of your site, make it unique and give readers a reason to read and you'll get plenty of traffic. There really isn't any reason to get your blog it's own domain. Especially if your current domain has been around awhile.
For SEO purposes with blogging, www (dot) yoursite (dot) com/blog or www (dot) yoursite (dot) com are same thing. But I personally prefer www (dot) yoursite (dot) com than www (dot) yoursite (dot) com/blog.
I run www.Scorpiono.com, but I also run blog.mylol.net - converts really well with website.com/blog Any combination is okay IMO, not a big traffic issue, just stick to good content & promotion.