Ideally yes, realistically no.
1. I don't think animals should have protections equal to humans. In first place, it would be pointless at best and counter-productive at worst. I mean, animals would be unable to appreciate such protections as freedom of expression, freedom from slavery (ownership), property rights etc. Legal protections should extent punishing deliberately causing or deliberately exposing animal at significant physical injury, or mental distress that would have significant negative impact on well-being of such animal.
2. We yet have to address and solve some of uses of animal products in society in the first place. For an example some of the pets like cats are obligatory carnivores and from I'm aware there is no solid research done that would establish vegan substitutes as suitable food for such animals.What leaves you in a predicament if you want to ban methods of obtaining such food, there are 2 options. You'd could to attempt feed such animals with vegan food, such experiment would in all likelihood go poorly.You could also release such pets to the wilderness/streets where they would fare very poorly due to not being adjusted, exposed to many dangers, disturb ecosystem and in case of urban environment cause issues in the society, not to mention many people would be quite unwilling to get rid of their pets.In addition to that, as wonder pointed there are many products in society that are created with animal product, so important questions need to be asked are there substitutes that could be used to create product, how important is the product in itself, how effective such non-animal product would, what are the costs compared to animal version of the product and if non-animal product can be reliably produced to satisfy demand.
3. I don't think there is a reliable evidence to conclude that everyone would be able to preform satisfactory on a vegan diet and some research does point to a correlation with higher risk of suffering from some mental illnesses such as depression on a vegan diet. We don't know cause of that, so we can't rule out possibility of significant increase being caused by diet. Not to mention in terms of anecdotes fair number people do claim to suffer from negative effects while on a vegan diet, whether due to poor choice of food, eating habits or dietary restriction of animal products is another matter but can't rule possibility it may not be good for everyone.
4.As I've explained in other topic, presently population wouldn't go with it, politicians with such proposal wouldn't be able to get it done and their career as politician would likely be over.
There are more issues that could be brought up such as regarding environment .
I would say there are a lot of questions that we need to answer and issues to address before deciding on such change.