Duty Officers do not gain experience and do not level up. The experience listed as a reward goes directly to you. If you want better duty officers you'll need to improve your experience in the various commendations and get the free duty officers that come with it as a reward.
At the home worlds (Earth and Qo'noS) as well as on the academies of both there are recruitment missions that you can do to get additional duty officers.
I don't have any duty officers to trade. People probably look for purple ones since they are the best.
If your really interested in getting more/better Doffs, I have some advice.
Spend a lot of time in Starfleet Academy! There are two officers there, located near the Lore daily contact, that you'll spend a lot of time at. First is the Personnel officer who controls the recruiting missions. Do these as often as you can. Most of the Doffs you get from these will be white, but you'll probably get at least 1 green from each. Most of the recruiting missions take about 24 hours or more to complete, so be patient. After you start those missions, exchange some of your officers for next higher quality ones. 5 to 1 exchange ratio, and about 10 dilithium(I think) for the exchange as well. The 1 DOff you get is of random profession, so make sure you don't take all 5 from the same profession. The recruiting missions should keep you in constant supply of common DOffs, and the exchange program will allow you to convert them to higher quality ones.
As you progress through the commendation ranks, you'll earn free DOffs from the DOff store. That's the second contact, who's desk is right behind the personnel officer's desk. Click through all the specialties, and if you have a free DOff token, you'll see it at the bottom. If you've got 2000 or so dilithium to spend, you can also buy some pretty good DOffs from this store too; though I don't do that. Using this method, it won't be long until you get everyone on your staff converted to green or better!
Combine this with the exchange, and you should have no problem getting all the DOffs you will ever need!
FYI, that Purple Exocomp DOFF loves to go out with the boys in the Drinks on the Town mission.
Also, if you look at what's available from the Academy Personel Officer, you will sometimes see DOFFs of all levels for sale for Dilithium. It's 1000 for Green, 6000 for Blue and 12,000 for Purple. That means it's cheaper to use five Greens to trade for a Blue than it is to buy the Blue BOFF directly. It also means that it's way cheaper to buy a Purple if you have the Dilithium to do it than to trade five Blue BOFFs worth 30,000 Dilithium for a Purple worth 12,000.
