Who is the target audience? Where? What's your objective? How will you measure success? Are you selling anything, or is this just a diversion/hobby for you? Do you have a business plan? A marketing plan? It's hard to be clear about who you are when we don't have more information.

Have you done any market research into the kinds of issues pet owners are searching for online?

Are you targeting key phrases that have high relative monthly search volume and for which there
are few competing pages for those specific key phrases?

Are your categories and article titles closely aligned with or a direct match for the terms that people are searching for online and is our domain name matched to a well searched for term? And are your articles optimized for specific search terms to a key word density that matches the preferred densities of the major search engines?

If not, you might be putting the cart before the horse.

You MUST choose search terms that you can rank for easily. With the best will in the world, if you cannot out rank sites with a PR value of 3 or less your site may never surface on the first 3 pages
of the most popular search engines.

First result from a common keyword phrase search is "Dallas Dog Life".
http://dallasdoglife.com/

It seems like a good name. If it was still available as a brand name and a domain name, would you use it? If no, why not? Your answers would be included in a creative brief.

Republic of Pets
Big D Pets
Lone Star Pets

Pet's Post. So interesting, even your pets will be reading it
Cats n' Dogs

On another tack, you have newspapers - what are your readers most interested in? Why do they read your newspaper at all in an age full of them? What are your current names (even if you allude to them generically). I'm trying to tap into the market you've already developed to give your magazine the sort of name people already like - or work out from that point.

Dog's Meow

Where cat & dog lovers go...