Considering dogs were in space before humans, I think they'll be allowed.
If we can solve all the other problems with extended space travel we can find a way to bring our dogs with us.
That reminds me of a story I once read about a very excitable space ship commander. The ship was returning to its base and the commander reasoned that an inventory might be required, so he set the crew to making sure every issued item was accounted for. Well, they couldn't find the offog. What's worse, nobody knew what an offog was. So this poor guy is going crazy trying to figure out what an offog is without exposing his ignorance to the upper command. So he reports the offog destroyed in a space warp. Suddenly the entire fleet is put on alert until this incident can be investigated. It turns out the inventory list was misprinted and should have said "off. dog", the official dog mascot.