About 5 years ago, my DH and I bought a 28 foot TT (used) that we still own and tow with a Toyota Tundra -- so, a bigger setup than you have or are considering.
At the time, DH was about a year from RE and we were considering my taking a year off and throwing ourselves and our to-be (at the time of RE) 4-year old son into the vehicle (exact plans for the pair of 60# dogs were hazy) and driving around the country.
After buying the trailer, we did a weeklong summer trip, which was lovely, and a two-week winter trip, which was enough to convince me that spending more than 2 weeks camping (even in a comfortable trailer) with a 4-year old would result in my strangling the 4-year old. Plans for the year seeing the country were abandoned; we have kept (and very much enjoy) the trailer. The longest we have stayed in it is 2.5 weeks. For us, that is enough (winter trips are harder than other times of year, mostly because of the limited daylight, but the basic principle remains the same).
Now. Your 19 months is not 3 years old (or 4, or 5, or ... we've gotten to 8), your kid's not my kid, you're not me, and on and on. But count me among those strongly recommending that you try a few shorter trips to decide if this is right for you before setting out on the road (while I 100% concur that renting RVs is costly, renting a tow vehicle particularly for a trailer as light as the one you're describing, may be a plausible option -- I don't know).
Also, no idea when you are planning to travel, but travelling with dogs in the summertime can be tricky because of the heat and not being able to leave them in a vehicle. We take ours other times, but leave them home in the summer. Something else to make sure you've thought through.
All that said, we love our camper and have done a bunch of fun trips. Hope you're able to find something that works for you.