In my experience there's not a lot of pre-preparation you can do with the child at that age; it's hard to understand the concept of 'future' at 3. Tell her that you're going on a trip, but focus on things you can do during the trip for the most part.
Daily or nearly daily calls are definitely one key element, in my experience; while neither my wife nor I was ever gone for a month, we did have multiple day absences around that age, and a week a couple of times. Facetime or similar video calls, or even just phone calls, work wonders.
One of the hardest parts of that long of a separation will be your wife not having a backup when things go awry; difficult bedtimes that you'd normally have switched off during no longer have that option, and there's no second option when it comes to discipline when one parent is stressed from a tantrum. My wife was gone for three weeks earlier this year, and I and my children (5 and 7yo) managed pretty well, but this was definitely the hardest part - I was lucky (in a way) that we'd had an earlier week apart a few months prior, so I had already had sort of a trial run learning how it was going to be, and was better able to manage the stress the second (longer) time.
That stress has a substantial impact on both parent and child, and will probably be much bigger than the "missing daddy" element, at least in my experience. Make sure you've talked over this aspect with your wife, and it helps a lot if she has a grandparent or friend who's there to help out a bit- maybe take your daughter for an evening or something once a week to give some separation, especially if she's a stay at home mom and there's no preschool (so no time with adults otherwise).
When you're away and having phone calls, I found it was most helpful to talk about two things - what you (and she) did that day, as that grounds the experience for the child; and what you're going to do when you get back, as that helps reinforce the idea that you're coming back, and there's something to look forward to.
I'll leave some articles here that are worth reading, some of which confirm details of above, some having different strategies.
This Boston Globe article, "Preparing Kids for when Parent Travels", confirms that children 3 and younger don't really understand future times well; it also suggests that it can be a good thing (as the other parent gets more bonding time), and you can phrase things that way ('you get special mommy time!'). It also agrees with your 'advent calendar' type reminders idea.
This article from Today's Parent, "When Parents Travel for Work", gives some great ideas, such as a Toddler Wallet (just like you might keep her picture in your wallet, she can keep yours in hers). Storytime videos also seem very appealing - while I'm a bit creeped out by the Facebook commercials recently on TV, the idea of recording a video of me reading a story so it can be played at bed-time makes a lot of sense and is something I've thought of before. The idea of a countdown - such as using a calendar with X's or stickers, showing which day Daddy comes home - would work well with my children, I'm not sure if that's beyond a 3 year old or not, but might be worth a shot.