/Thanks for your comments, Timothy. Well, the poem is not only about dogs, except about their ability to inspire love and to love unconditionally--like God does. In that way, dogs are better than us. And the other linkage is that they are, as I'm sure you know, mirror-image words. I am juxtaposing the God/doG word-play to point out that the Highest and one of the lowest of creatures are better than humans but, for some reason, they love us anyway. So it's really about love, and about how strangely we love, and how we're less forgiving than both God and dogs.
The part "And Thank God/and thank Dog!" follows the line about love comes in the window even when we lock the door. Love tends to get to us anyway, even if we're determined to protect ourselves, even if we think we can't risk it or don't have time for it or don't trust it, or whatever. Love will find a way to sneak into your life even if it is only through God sending you a series of dogs to love. (And let us be thankful to both of them for that!) I also tried to say (in the part you liked most) that we always think the our current love (whether it's a lover or a baby or a dog) will be our last because we just can't imagine ever loving anything more than that! But we always come up with more love, even when we think we've used it up. So really, I think too much description of the dogs would further camouflage the message, which, given that you didn't understand all of it, means it may be too obscure already! But I'm glad you liked it anyhow, and I appreciate the feedback!