Without seeming too stalker-ish, I looked at your past posts and it looks like your camper is a Rockwood Mini Lite 2104S
The biggest challenge that you're going to have with a family of that size AND a dog is finding a vehicle with enough payload capacity to carry you all, your stuff and then the tongue weight of your camper (at full load would be 475-700 pounds (i.e. 10%-15% of the gross camper weight)).
You are going to need to make a conservative estimate of what you all + dog weigh, what your stuff weights that you carry with you in the vehicle and anything else that you can think of.
Basically, the vehicle that you buy needs to have enough "cargo carrying capacity" to support you all, your stuff and that tongue weight estimate above.
If you're willing to go to a scale, it can tell you all sorts of things to help you make an educated decision.