I have a brother mfc-680dw Driverless and have no problems both print and scan. If the MFC-J1300DW is Driverless it shouldnt have any problems tho i to had to add the brsaneconfig4 and set ip for scanning. I have a desktop and never put it to sleep or anything. you need no other drivers except the brsaneconfig. The point of driverless printers they have one standard thats basically plug and play to have some normality to these printer issues nowdays. Sounds like problem may be elswhere and not with printer/scanner. I will check mine out sometime when i have time.
Found this maybe there is something like this in linux
Fix – Brother Printer keeps going offline when the printer goes to sleep?
To fix this issue, you can adjust the offline settings by pressing the ‘Windows + Q’ keys. Secondly, you need to type ‘Device and Printers’ in the search bar. Now, locate the Brother Printer model and right-click on it. Further, you have to choose ‘See What’s Printing’ option and then right-click on the new print queue. Here, you should clear the ‘use printer offline’ settings. I will have to research mine abit.