Katarina has a particularly safe laning phase, simply because she has long range last hit tools and a blink on a short cooldown. If she never initiates on her enemy or over extends, theoretically she won't die in laning phase. Combined with skill cap this can be abused, simply by Poking and being invincible at the same time: i.e. Casting Q on the caster minions of a wave ultimately bouncing onto the enemy champion or getting in melee range of an enemy champion, Q Wing them and Shunpoing (E) away.
SO
I suppose you could call her a good 1v1er in the sense of laning.
However, late game when she has full build, she has difficulties winning long trades against champions with CC or lots of resistances that can keep her on her toes for long times. So Tankier enemies, like Nautilus will win 1vs1s because he will just never die and kill Katarina with 50 damage autos, while a champion like Kog'Maw will be instantly deleted by her insane burst.
SO
Late game, I suppose you could call her a good assassin, in the sense of eliminating squishies.
IN YOUR CASE, against Udyr mid, that lane could go either way but ultimately goes off flaws made by the Katarina.
I would say, practice her, primarily in the laning phase, because it makes late game so much easier as well.
Hope this helps :)