There are many ways to build Dominators, it all comes down to what concept and intended use/ play-style is. Pets aren't mandatory, but they 'can' help and are a decent power to slot in 4 pieces of a set for recharge bonus.
There are those that get Fighting or Fighting & Leadership to bolster their survival, but the downside is added strain to to an already Endurance intensive AT when Domination isn't up to replenish it. Your Controls are your best defense and damage resist, imo.
Yes, you can crutch Incarnate powers to help, and it is an option if needed.
I tend to make my Doms Perma-Dom and fairly exemplar friendly and they do solo fairly well.
In that, Dominators are late bloomers (Plant/ is an exception to a point) and can struggle with EB's and AV's. I tend to avoid AV's, but there are those that fight them and tune their builds to do so.
I'll include a Mid's EXAMPLE template, of one way I could build it, with your requirement for the Experimentation Pool, and you can see if it helps you with a build.
There are some Powers. Epic pool included, that are essentially mules for things like LotG global +recharge (Maneuvers is one, since I never run it), so keep that in mind.
I chose sets with the intention of going Perma-Dom and bolstering Hit Points and resistances a bit, to soften some stray attacks that get thru.
Template-Dominator (Plant Control - Fire Assault).mbd