Do you have to install a regulator? No
Is it a good idea for your installation? That depends. So far, the suggestion I've heard is that if the pressure is over 80psi then you should, but you're boarderline. So the design of your system would dictact if you should/can install a regulator or not.
Here's some pressure losses to keep in mind:
1. I seem to recall reading something that said a pressure regulator must be set so that the down-stream pressure is 15psi below upstream pressure or more. So if we round up your pressure readings to 80psi, that means your system starts at 65psi.
2. You then have to deduct pressure loss through your water meter (1-5psi depending upon meter size and designed gpm). As an estimate, let's assume 2psi, so now we are down to 63psi.
3. Backflow preventor: if you use a PVB or DoubleCheck Backflow preventor, you'll most likely loss about 5psi (depends again on flow rate and device specification). So now we are down to 58psi. But if you use a RPZ Backflow device (the best thing to use, and a must if you plan on installing a vertilizer injector) then your pressure loss through it could be anywhere from about 7-15psi (again, depends upon your flow rate and the specific device used). Assuming a typical 12psi, then you're down to 51psi.
4. The next location for pressure loss is the valves. Again, you have to check manufatures specs to know exact pressure loss for your design flow rate, but I would expect the losses to be around 2-5psi. So this means that your down as low as 46-48psi left.
5. The next pressure loss to think about is the heads themselves. You need about 30psi at the heads for sprayers and 40psi or better for rotors. So if we use worse case so far (rotors and a RPZ) then that leaves only 6-8psi losses MAX in the pipes themselves (sounds like you'll need some really large pipes, for both the main and the laterals). However on the other end (sprays and PVB) and assuming low end pressure losses for everything else, you could have as much as 26psi of available pressure losses for friction losses in the pipes.
So in the end, again it depends. Because you're below the 80psi suggested point for when to use a regulator, I see it as not required. If your design calls for lower pressure losses (such as PVB with sprays and we don't have great distances to go) then you've got "extra" pressure to work with and the regulator will reduce the stress you're system will be under. But if you want to use the RPZ and rotors, you don't have any extra pressure to play with so you're better off skipping the regulator.
So my bottom line suggestion is to design the system without the regulator and determine all you're pressure losses. If when you're done you've got an extra 15psi, then add the regulator. If you don't, well obviously you can't.