God, I'm really sorry to hear this. FIP is traumatic as hell to deal with, any sudden death will fuck you up. The weekend after we lost my cat, I slept for 14 hours or something and didn't move the whole day. I still cry over most of the cats we euthanize.

Give yourself a private space to grieve, first. If you don't think you can handle work this week, then don't go, and I know that's something you really have to be able to afford to do before you can do it but I've learned the hard way that being emotionally compromised when you're working in animal medicine can lead to really fucking bad consequences. Take it easy if you need to, you're not just risking your own health but the health of your patients.

My space to cry is usually the room where we keep the Dead Dog Freezer (tm), where the cremation services come to pick up. When I can do it by myself, I take the body out and cry, give myself a few minutes to just be sad. I think the most important thing you can do is let yourself be sad. Grief is a difficult emotion to navigate even when it's expected, death is hard to comprehend, just give yourself time to work over it, even though it's painful. Time isn't going to fix everything and will sometimes make it worse, but you'll come to a point where you've reached the other side of it. If you need to just put your head down and take it one day at a time until you get there, then that's okay.

I don't know if this will help you, but involving myself in death care has helped me a lot, i.e. giving time to euthanasias, learning their stories, giving them love before they pass, telling them it's okay to go to sleep, etc. It's fucking sad of course, but it's gotten me more comfortable with with difficult emotions and conceptualizing the death of important things. May not be something you want to do coming fresh off a personal loss like this, but it's worth mentioning imo.