Update 13 Dec 2014: Turns out I was right to seriously question the veracity of the story and its lack of credible sources: http://www.religionnews.com/2014/12/12/sorry-fido-pope-francis-not-say-pets-going-heaven/. Still, the points made below are valid. :)
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As the NYT and America article allude to, the short answer is no. The Pope made an off-the-cuff remark to comfort a child. He did not "declare" anything, much less define it infallibly (ex cathedra). I am typically not one to go around trying to reinterpret the Pope's words, but the brouhaha ensuing from so little substance here is just too much. (And also, a friend of mine asked me to share my thoughts on this blog.) So here you go. ;)
Doctrinal authority/certainty is a very nuanced topic in Catholic theology. There are degrees of certainty with regards to Church teaching. I try to summarize them in a prior post on this blog about theological grades of certainty. I really do recommend reading it, not because I think my writing is awesome but because I have used reliable Catholic sources to help summarize the subject. I won't restate it all here. If you read it, it will definitely help you understand where the Pope's remarks fall in our view of things.
Now back to the subject at hand.. Certainly we can hope and wish that we will somehow be reunited with our loved animals, but that is a far cry from making any kind of authoritative definition on the matter. Personally, I could see such a position being more plausible with regards to the General Resurrection than to heaven--because that is bodily resurrection, and it would fit better that some animals we love could be bodily resurrected (without implying that they have immortal spirits/souls, which I think is pretty indefensible from a Catholic point of view).
Many people get pretty sentimental on this topic, but sentiment is not a good way to discover and understand truth. Many say, "if my [pet] isn't in heaven, then it isn't really heaven, and I don't want to go there" or some such. I would suggest that these people ought to be more concerned that they themselves make it to heaven rather than worry about their pets. It is not a little presumptive to treat the question as if it were just a matter of what we would like our own personal heaven to be like. St. Paul cautions us to "work out our salvation with fear and trembling." We are not even assured of our own presence in heaven, so to make definitive pronouncements about the presence of our personal pets seems a bit off, to say the least.
Let me put it this way. Traditional Catholic teaching--which is founded in centuries of solid Scriptural, theological, and pastoral reflection and shouldn't be easily dismissed based on personal whims or desires--is such that 1) animals are different from us; they do not have immortal souls like we do, and 2) neither do animals have moral faculties (and so neither can sin nor need redemption, in the sense of from personal/original sin). 3) There is, to my knowledge, very little foundation in our Tradition to claim that individual animals (e.g., my pet cat Aelfric) will be part of the Resurrection, much less in heaven prior to that as some sort of spiritual being.
So anyone, the Pope included, who wishes to offer a theological opinion to the contrary, has a lot of work to do to provide support for such an opinion. And for it to be taken seriously, it has to be more than "because I want my pet" or "because it wouldn't seem fair" or "because it would make little Johnny sad" or anything like that. It has to be more than some vague belief in God's goodness or broad extrapolations from a phrase or two in Scripture. It should square and be reconciled with what we do know as definitively revealed (see theological grades of certainty) and ideally fit well even with less definitive teachings.
IN ANY CASE, characterizing the pope's off the cuff consoling remarks to a child as some dramatic change in Catholic teaching is nothing but absurd sensationalism.
As I said, while many would classify me as a conservative (though I see myself as a firm centrist), I am not one of those purported reactionary conservatives who feels threatened by Pope Francis. I love Pope Francis. I love his pastoral style. I love how he challenges my preconceptions and makes me reconsider them. I love how he leads by example. I love how he emphasizes Gospel witness.
I also love Father Benedict, and Pope St. John Paul's writings (especially Evangelium Vitae) were instrumental in my joining the Church. Despite ignorant characterizations to the contrary, the traditional Catholic position on this question of animals going to heaven or not (and related considerations) has absolutely zero to do with some kind of animosity towards creation, nor is it some weird desire to feel special/different/superior to the rest of creation. It is simply a matter of thinking through the consequences of what we know of Divine Revelation and nature itself.
