Qualifying with only retirement income

I plan to retire next summer from my job with the federal civil service. My wife and I plan to buy a house in northwest Arkansas. We currently live in Arizona. My wife is already retired from civil service. We are both covered under the old civil service retirement system, which pays a straight percentage of our income after retirement.

I currently  make $70,000 per year but will drop to $41,000 after retirement. My wife's retirement if $1050 per month, which will give us about $4400.00 per month. We have no debt payments of any kind. We will both have fico scores over 700. We want to buy a house in the $120,000 to $150,000 range with $40,000 down. I think this if sufficient income for this price range but am concerned about qualifying. I have worked in my job for thirty years, but will no longer have it when applying. Will the new retirement be considered like a new job? We want to buy a house as soon as possible after retiring. This government retirement system is probably the closest thing to guaranteed retirement available now, probably more secure than social security, but it will just be started when we apply.