If she is a hatchery RIR I doubt she will go broody but she may. Since she just started laying though I would doubt she would go anytime soon so I would collect her eggs. Now if you want to see if she will go later on say after she has been laying a couple of months then you can leave her eggs for a week or so at a time to see if she will set them. I have had barred rocks, pro reds and brown leghorns the last 7 years for my layers and have NEVER had one go broody. Just bought 25 new pullets of different breeds and most likely of those breeds all will go broody on me since they are know to be broody breeds even for hatchery birds.
Yes she will continue to lay where she is laying now unless of course she isn't laying in a nest and is just laying where ever she likes. TO help her remember where you want her to lay get a fake egg to leave there all the time.
