I also made some deer related puns. Laughed it off pretty much. I also contrived a whole situation whereby I had actually planted the deer in the road (made from fibreglass and on a trolley with wheels), and then used a stunt double to run it over in my car as I had just met my mum's new boyfriend that evening and it was all an attention seeking exercise

Some interesting life lessons:
1) I had breakdown cover I took out with my car insurance - but they won't recover you in a traffic accident. This resulted in an interesting phone call when I got put through:
RAC Lady: Hello, how can I help?
Me: I've just hit a deer and I'm looking to have my car recovered
RAC Lady: Ok, well your breakdown cover only covers you for mechanical breakdowns, not for traffic accidents
Me: Well in that case, my car won't start!
RAC Lady: *laughing* Sorry, but you've already said you had a traffic accident
Me: Well, worth a try

(yes...you can wink over the phone)
RAC Lady: *still chuckling*
She was totally flirting with me... also, at one point she thought I'd said I'd hit a girl, not a deer, I was 'oh good god no!' - like I would have called the RAC to get my car recovered before the police/ambulance in that situation.
Also..with my insurance company when trying to see if they would recover it:
*normal standard reporting a claim information exchange*
Insurance: Well as you're third party only, we won't cover you in this instance
Me: Well I guess the deer probably doesn't have insurance, so I can't exactly claim off theirs!
2) If you kill a deer on the road - it's not you, but the person behind you that gets to keep it - this is to stop you from deliberately killing them for meat.