My T is becoming a LMFT but does have 20 years as a social worker specializing in trauma.
Are you good with regulating yourself? In other words, when you start to have intrusive memories, or thoughts about the trauma, can you keep yourself grounded without help?
And, does your therapist know your entire trauma history, or just this recent event? Is she suggesting EMDR on the recent event, or on your entire background? They generally prefer to go back to the first trauma, chronologically; however, if there's no significant relationship between your recent trauma and your history, and if you are not suffering any PTSD symptoms connected to your history, then that makes things a little more straightforward.
(What you risk is that, in processing the current trauma, you awaken issues that source from your past trauma. That would be a mess.)
I think if you feel solid in your own regulation skills and stability, and you are not affected by your past trauma in a way that relates to your recent trauma, and your therapist knows your entire history in detail, then it could be worth giving it a try. It's a fair question to ask her how her resources are, if she needs to consult on your case or needs supervision.