Welcome to the Forums cmcolla77...and soon to the RV Lifestyle
I am going to chime in X2 on the comments about trucks and rigs. You have a unique opportunity to learn from our mistakes
Almost every one of the experienced RV'ers on the forum have made the progression from PUP->TT->5er (and some go on to a MH
The idea of rent before you try is a expensive option but not as expensive as buying a rig and then realizing it does not fit your needs!
Perhaps this is the way you should go.
Given your Furbabies (what a lot of RVers call their animal companions) you might want to look into a Motorhome (MH) that will solve the problem of where the pooches live while you travel. The downside to this is a large MH can cost as much (or more!) than your home!
If you are set on a truck and trailer rig, I agree with the others - just get a 1 ton truck and be done with it. Assuming you are going to keep the 1T until the wheels fall off go ahead and get the diesel (your break-even will happen at @ 108K miles), and if the truck is not your Daily Driver (DD), strongly consider getting a dually (dual axel). Then you can tow anything!
Getting a MegaCab (Dodge RAM) should provide enough space (with the seats up - or maybe even removed) for your furbabies.
What to tow? This is just my opinion, but get a fifth wheel (5er). SO much easier to pull than a travel trailer (TT), no sway, not susceptible to Semi vortex, and with that 1T Dually yanking it down the road, you will not even know you are towing anything...well maybe if you opt for a 44' toy hauler you will notice a teensy bit.
Hope all these posts help you with your happy RV decision. Again, welcome to the club, and ask questions - this forum has an amazing knowledge base!