I have an old Rock Shox fork that I want to replace with a rigid fork. The Rock Shox is 1 1/8 threaded. I can change that to a 1 1/8 threadless as long as I change the headset, right?

Yes, but you'll also need a new stem. Don't forget that you'll need a fork at least two or so inches longer.

That is what I thought. I already have the stem so I will need a threadless headset. And the steerer tube is really long so that will work fine.
Another question: The rigid fork I am looking at has a axle to crown measurement of 395mm. I measured the Q5 and it measures 410mm. I measured from the center of the axle to the base of the steerer tube.
Will this cause a problem in handling? The fork rigid fork description indicates it is "suspension corrected" so I assume that means it is allowing for the bit of sag that a suspension fork has when I am on the bike.

The fork is close enough. It's hard to nail the sag on a suspension fork so the "corrected" forks are based on a best estimate of the neutral length. When you set this up measure the fork based on 40-50mm of spacers and make the cut. Then you can move the spacers above or below the stem until you dial in the final height (general guideline is no more than 40mm spacers below the stem).

Once you have your final stem height set, it up to you whether you want to trim the fork to final size, or leave the extra spacers above the stem keeping your options open.