Buy some decent concealer and drink strong coffee. I work 4 days a week, ds always wakes at least once (and the past few days has been ill so we've had almost no sleep!).
To be honest, I find work much less tiring than being at home. Once I get to the office I perk up and forget how utterly knackered I am.
My absolute top tip? Cycle to work. Sounds crazy, but it really perks me up and gives me enough energy to get through the day. Bike seat on the back for the nursery run, then in to work. Depends how far your commute is - I've got a 4 mile cycle from home to the West End, which is do-able in 30 mins. Has the added advantage of meaning I know exactly how long my commute will be, as I'm not reliant on public transport.
Avoid stress and be organised. That is tiring. Have good childcare, shop online, plan ahead, use Google calendar so you both know where you are and who's doing what at any one time. Stock up on birthday presents and cards so you're not panicking at the last minute. Etc etc.
Honestly, when it comes to it I think you'll find it much easier than you think. If you'd asked me 9 months ago how I'd cope with working on the back of 4 hours sleep, I'd have said "not well". But I manage. Not brilliantly, but I manage. Keep telling myself it won't last forever....