Having the two passports yes is ideal. What I have heard, when it is getting a little hot for some, they enter on their "other" passport as a tourist. Then if push comes to shove "see ya later".
Question is in that circumstance, goes without saying that you won't be welcomed back in Doha. What if you went to Dubai or Oman on holiday or tech stop. Would they send you on an all expenses paid one way ticket to Doha?