I was just about to accuse you of making a false claim, because when one is on Bible Gateway’s Keyword Search, it does not allow them to choose the Douay Rheims from the pulldown list (at least not on my computer!).
But then I checked Bible Gateway’s available versions, and saw the Douay Rheims listed (and I was surprised to find that some of their texts even have the “Apocrypha”).
I took note of the fact that each version is numbered, and the Douay Rheims is number 63. Therefore, if one visits Bible Gateway, and wants to search the Douay Rheims (but, like me, is faced with it not being in their menu), they can search for a word in any translation, and then change the version number (“version1=XX”) to 63. For example, here is how the word “holocaust” appears in the Douay Rheims as per a Bible Gateway search:
(In case others are wondering, I chose that word because it strikes me as being distinct to Catholic translations).