Rather than a simple answer or gut feeling, l would like to have some facts to back up this decision. Can you help?

No. Airlines are risky, but Southwest is probably the best of the bunch.
Fuel costs can make the airline business too risky. Right now fuel is cheaper so it might do OK for a while, but if oil goes to $150 per bbl, then Airline stocks nosedive.

It is hard to tell by past performance. Southwest may have avoided the effect of the price run up by investing in the futures market, but that can also result in losses if you buy futures and the price declines.

Their value ratios r better than average for airlines.
Their P/E is 15.83.
Their Price/Book is 1.12.
The average airline Price/Earnings is 32.73
The average airline Price/Book Value is 2.58.
http://biz..com/p/airlinconameu.html#ual
http://finance..com/q/ks?s=LUV
Their 5 year average return on equity is 7.78 percent
They will not do well if the price of oil goes up much more but they have not had any quarters with negative earnings recently.

Yes, but only within an index fund. For example, the S & P 500 index holds .10% of SW Airlines.

You should hold a diversified portfolio & holding any stock alone is very risky.

Here r concerns about this airline:

Should profit-sharing & stock compensation growth stall, employees might use their union muscle to demand higher wage increases & diminish Southwest is cost advantage.

The growth of other legitimate low-cost carriers is making it harder for Southwest to pluck attractive routes from the hub-and-spoke carriers, thereby making profitable growth a greater challenge.

As the average tenure of employees at Southwest has grown, labor costs per available seat mile have risen, & eventually productivity improvements may not keep pace.

Despite fuel hedges, oil prices remain a wild card that could hurt the airline is bottom line. Southwest is exposed to cyclical risk in the economy because air travel is highly correlated to economic conditions. Eventually, the quest for growth (as demanded by many investors) may necessitate head-to-head battles between the best low-cost carriers: Southwest, JetBlue JBLU, & AirTran. Such a clash of titans could result in devastating price wars.

The low-cost carrier business model is particularly vulnerable to higher oil prices because it depends on expanding the airline by stimulating demand with low fares that attract customers who could not otherwise afford to travel by plane. The price elasticity of demand for air travel is high, & the low-cost airlines r particularly at risk of destroying demand if they raise prices too much.