Ok, can we get past the stupidity with Tarrasque style fail and accept that the fucking dragons are not Dominate bait due to immunity already?
No, looking at dragons statted out by wizards in the Draconomicon
CR 14,16,18,19, 20, and 22 black dragons do not have protection versus dominate monster.
CR 19+ Blue dragons do.
CR 21+ Brass dragons do.
CR 21 and 23 bronze dragons have mind blank.
Copper has no protection.
Gold is well protected with it having pro evil from CR14 on.
Green lacks protection at CR 21
Red is lacks protection at CR 20, 21,23,24 and 25
Silver lacks protection at CR 18, 20, 21, 23, 24, 25
White have protection at CR 17
Dragons seem to value True Strike, Magic Missile, and Color Sprayl more than I would expect.
So by no means are dragons as a group immune to Dominate Monster.