A reliable method to confirm a screen or other hardware fault is to take a screenshot when the fault is evident - and then review the captured screenshot image...
When reviewed, if the line is not present in the screenshot image, then you have demonstrated that you have a hardware fault that, sooner or later, may become sufficiently severe that repair or replacement of the iPad are the only options. If the line is visible in the screenshot, the something other than hardware will be the cause.
Note: When reviewing the image, rotating the iPad screen orientation by 90°, from Portrait to Landscape, will ensure that the image does not coincide with screen defects if present.
Take a screenshot on your iPad – Apple Support
If you have a hardware fault, your one month old iPad is within warranty - and should be repaired or exchanged by your retailer or Apple. If your iPad requires repair:
iPad Repair - Official Apple Support