The best way to advertise your blog is to post content regularly and share them in various social networking websites. This will give you more visitors for your blog post and build your blog popularity online.
This reminds me of my plan to create a blog of my own. But blogs about pets are a dime a dozen so I am reluctant. As per my research, there should be an ample number of potential readers among your circle. They will serve as your spark plug for the initial issues. The updates needed to be regular like weekly at the least and daily update is the best (although tedious). With the popularity of social media, it's easy to advertise especially if your close friends would help you spread the word about your blog. Lastly, the theme should at least be interesting to a majority of people.