Ex and I split when DS (11) was a toddler and DD (19) was 9. He sees DS EOW for 9 hours (when he's not on holiday with his "new" family) - but not DD, who refuses point blank to have anything to do with him. I'm the 24/7 parent, the one who gets up in the middle of the night to deal with poorly offspring, who ferries them around, who listens to their tales of woe, who has their bed invaded if and when nightmares occur... and all the other minute details of being a hands-on parent.
Although I have always said that if ex wanted to see them over the festive period, we'd sort something out... neither of the DC have ever wanted to. There is no alternating, there is no shared December 24th, 25th or 26th, and any gift exchanges happen on the following weekend day that ex is due to spend time with DS. This is their choice, incidentally. Ex's and the DC. Personally, I think I'd actually quite like a break/to do what I want to do for a change... especially as I loathe Christmas, and always have done (even when I was a small child I couldn't really see the point in it!). This year, the EOW falls on Boxing Day and when I mentioned this to DS, in a "isn't this brilliant?" sort of a way (secretly thinking that I could spend the day in bed eating chocolate and being lazy!), he became very upset and point blank refused to entertain the idea of spending the 9 hours with his DF's family! I'm not going to force him to do something he has his heart set against - particularly not as we're entering those tricky years where he needs a relationship with his dad in so many ways...
Conversely, I have friends who have split/divorced who do alternate their Christmas' and it seems to work out brilliantly for the children. Not so much for the parent not spending the day/time with the children, but... at the end of the day, it's what's best for the children/what the children want that counts, isn't it?
As your DD grows, she may or may not want to alternate Christmas with your ex. Although, he may also change his mind as time passes. Be prepared for either, and remember that it's what's in the best interests of your DD that counts. Not you. Not your ex. But your DD.