If you are leaving Qatar permanently so your company/mandoob will ask immigaration to cancel your vissa, if it is cancled then they will stamp CANCLED on your RP on pasport so on dubai airport you can not get visa on arrivel,
If your company or mandoob did not ask Qatar immigaration department then they will surelly not cancel your visa automaticly.
May be your mandoob mean that after permanent exit from Qatar you can not get on arrivel visa on Dubai air port,
so better is that you must get visit visa for Dubai.