DD actually arrived early on Boxing Day morning.
I had a Christmas outfit, just in case. And a few stocking items - a travel sized sudocreme, buggy toy, rattle, cloth book, Christmas bib, that sort of small thing. If you want a "big" present, something like a collection of (either small books or a hardback bound version) Beatrix Potter or other classic book for bedtime stories for years. Or start a savings account.
Get a copy of "Twas the Night before Christmas" and begin a tradition of reading it at bedtime every Christmas Eve.
While you have everything else done, bookmark a website that has lovely "new baby" decorations and get a personalized one as soon as you have a moment. Or get ahead by buying something like a Waterford Crystal decoration for this year (i.e. with 2015 on it) - a once-in-a-lifetime heirloom could be worth the price.
Um, apart from arranging in your head what you will do foodwise (pre-ordering M&S or similar, teaching DH how to cook a roast dinner, agreeing which wider family household will feed you all). You could make a few things to put in the freezer - lots of regular dinners for DH and yourself (I found keeping seasoning and spices minimal was important but DD had reflux and I was bf'ing); and also a few things for Christmas dinner and season. Even things like HM mince pies or a log of cookie dough to slice and bake when you want something with a cup of tea.
I'd also, as they become available, try to book slots for online grocery shopping. You may want to get out, but you may want to get the basics delivered. But do a general stock-up of the cupboards (easy to make foods you both like, things for visitors, cleaning stuff, toilet rolls/binbags/kitchen towels etc), and especially the heavier stuff and non-perishables - mostly in advance but some in your online shops. So you can just go for a walk and wander in to supermarket for a bottle of milk and 2 chops, not have a faff about car seats, driving, baby trollies and do a massive shop while worried about you leaking/next feed/poonami etc.
And think about things like entertaining yourselves (nice DVD box sets, a good book that you don't need to concentrate on too much, Sudoku/crosswords/logic problems, board games etc). And making the house winter-ready, like having logs/coal for open fires, check boiler servicing, plenty of change for meters if needed, candles (both for atmosphere and if power out) etc.
Good pair of boots for you, and warm winter layers. And a good muff for Baby, and a buggy. So you can go out anytime it is dry for walks (and even in rain if right protection in place). Figure out about local public transport if you and DH share a car, so you can get places independently once he's back at work.
Overall, enjoy!!