Note: I am by no means an expert.
Congratulations on your new gun!
Assuming you're right handed ... and you typically see these low and to the right shots ... it could very well be a sign of jerking / pulling on the trigger or movement in your right shoulder.
While shoulder movement is hard to diagnose in a dry fire situation, dry firing while focusing on your front sight (where you should focus while shooting anyway), you should be able to see if your trigger technique causes any movement in the sights. If it does, work on finding out why and fixing it.
Only do this if you follow proper hang/no-fire rules!!!If a moderator feels this is dangerous, just delete this part
If you take a friend or someone else to the range with you, have them load a snap cap (or one of the 25 cent dummy rounds available at the counter at the BH) and then a random number of rounds in the magazine.... and then shoot until you run dry.
When the gun picks up the snap cap from the magazine, you won't be able to tell that the magazine is empty or that it has the snap cap chambered. Then when ya squeeze, it won't discharge, and you'll immediately notice if you're jerking the gun any while squeezing the trigger.... and prolly feel like an idiot if ya pull the trigger, the gun jerks, but no lead goes down range
When you hit the snap cap, follow standard hang / non-discharge safety rules -- keep it pointed down range for 30 seconds before clearing the weapon.You can't be sure if it was the snap cap or a dangerous round.If you don't have a friend with you, try to not keep track of the number of rounds ya load on top of the snap cap, or load a couple magazines with a snap cap in the bottom.
(off topic: in a revolver, leave one or two cylinders empty and gently spin the cylinder... don't be violent with it... cylinder alignment is a primary failure of revolvers).