In what key would this be?

In what key would this chord progression be?

D F#m A E

Maybe D major. Whatever chord sounds like "home" is the key the progression is in.

Play the D Ionian over it

A major (IV-vi-I-V).

Yes thats in the key of A there is no E in the key of D there is Em. Key of A is A Bm C#m D E F#m G#mb5
D is D Em F#m G A Bm C#mb5
You can play the D major just skip the 7th note the G because there is no G in the chord E. But it is easier to just play A major :P

By no E i mean no E chord