There is also an "e-gate registration" desk in T1 airside. So you could theoretically do it before going through immigration. Getting back could be difficult, however, unless you then proceed through immigration. (I guess you could walk backwards down the stairs and past the moving walkways, then up the stairs back to the transit desk. I have gone backwards though security in the T1 transit areas many times, no problem there, but I am not sure if they would let you walk all the way backward from immigration.)

Also I am not sure of the operating hours of this desk.

I also just discovered something interesting -- the Emirates Gold card with e-gate added doesn't work inbound at T1. I didn't try outbound, but will on Sunday. (The card also refers to "Dubai," so I assume that it doesn't work in Abu Dhabi.) I asked the immigration agent adjacent to the T1 e-gates if I could also get the old e-gate card (I am not a UAE resident), and he said yes. I didn't bother yesterday, but when I enter Dubai T1 next week I will try.