Does oxidation change the color of beer?

After moving an APA to the secondary it went from a cloudy yellow color to a clear brown that is darker on top.

Could this be due to too much head room in the secondary causing oxidation?

taste it and find out. if it tastes like liquid cardboard then its oxidation. next time fill the headspace with CO2.

im a fan of the dry ice method. get a 1# block of dry ice. you can find it at most Ralph's and if you don't have one in your area go online and look for a local distributor. break up the block into small manageable chunks then drop one in some warm water. this will generate lots and lots of CO2 rich fog. during racking pour the fog and only the fog into the carboy. you may need more than one chunk of dry ice and more warm water. then just before caping get a nice big chunk of dry ice and some fresh warm water and flood the head space with CO2 at the same time you are capping.

That's happening not because anything is wrong, but you kicked stuff up in racking over and it is now beginning to stratify as it drops out. In other words the beer is clearing. Also optics are strange due to the shape and thickness of the carboy. Just relax, tons of brewers daily rack theirs to secondary (those that still use one) and don't oxydize their beer. You are just showing typical new brewer's paranoia.

Short answer: no.

Addressing the technique: Racking a beer will release enough CO2 to blanket the brew and protect it from air.