Thanks all for your help. I went to UAE embassy today and asked them the same question. They told me that as long as I am travelling with my wife, she can get visa on arrival same like me as long as her passport is machine-readable (which hers is). They did not mention any condition regarding Qatar RP validity though. Anyway, by the time we'll travel, her RP will be around 6 months old and around 6 months left. So I hope there should not be a problem Insha Allah.

Thanks all so much for your help. Highly appreciated.