That is good advise in regard to your tow vehicle. Make absolutely certain, it will handle the weight of a "loaded trailer", not just the UVW (unloaded vehicle weight). Don't rely on the dealer's word of "oh ya, sure you can haul it", or on the UVW posted on the unit. I have never found the UVW to be accurate, as these are typically the weight of a base unit and model, and not actual weight of the UVW. You should weigh your tow vehicle, and weigh the unit you wish to purchase, if the dealer will not allow this, walk away and find another dealer.
At any rate, we had a Cougar previously and loved it. It towed good, the height was good, and it seemed to stand up very well.
Now that being said, I'm sure someone will post something they dislike about Keystone or Cougars
. But just wait until the others chime in about another "good" model and you will have a bunch more nay sayer's on those too
. I am pretty sure you will find someone whose likes, and someone who dislikes any model, brand, or type you choose or recommend. Yes, some are better built than others, but it does not guarantee a problem free unit. Confused yet? No worries, select a model that will be good for you and how you and your family wish to use it. Make certain your tow vehicle is capable of hauling it. Consider how you would load it. Is there enough storage available to you? Do you often need to haul it with a full tank of water to your destination, or do your typical destinations have fresh water available? Hauling with fresh water adds a lot of weight, so you may not be able to haul all the other things you want or need to take with you.
Going by the specs you have listed, and assuming your tow vehicle is capable, then I agree with one of the other posters that you should be looking for a unit with 7k axles as opposed to only 6k as I am sure by the size, and number in the family you have listed, you are going to have a fair bit of belongings to take with you.
Good luck in your search.