You have provided sufficient information for me to answer your question - YES!!
I have been 'camping' for more years than I care to admit - from a pup tent in Boy Scouts to a lovely Class "A" which is our present rig.
You, Wife and baby in a rig - perhaps - add the fur babies - NO WAY!
I expect you are happy together now - just seriously think about all of you 'living' together in a very small space for weeks / months. OK - if you think it is a good idea, then go for it, but at least you asked and I provided my personal opinion - and it is worth what it cost you - NADA.