Well, yeah, like so many Pokemon-that-evolve-by-Stones, Nidorina stops learning moves naturally when it evolves into Nidoqueen. However, it has one more move: Superpower at Level 43. But since it lowers Attack and Defense, I don't really like it.
For me, I'll evolve it as soon as Nidoran becomes Nidorina, since all of the attacks I have on this preferred set are TM-taught:
Nidoqueen @Leftovers
Ability: Poison Point
Nature: Quiet (-Speed, + Sp. Attack)
Substitute/Double Team
Focus Punch
Thunderbolt
Ice Beam
EV's: 112 Attack, 146 Defense, 252 Special Attack
BOAH-Queen, as I call it, since like TyraniBOAH and BOAHNite, it's a Skarm-Bliss counter. Boltbeam hits anything at least neutrally but Chinchou/Lanturn and Magnemite/ton, and they can be taken care of with Focus Punch. Since I find it rather hard to use the Subpunch combo, you can replace Substitute with Double Team since maximized evasion is really hard to hit if you don't have perfect-accuracy attacks, and those are not very common.