Here's how to check through Apple:
This is the Mac Print 101 article for OS X Lion and Mountain Lion. I hope you're using one of those. (I'm concerned because your post indicates a year-old iOS version for iPhone, and does not even mention Mac)
Click on the "Printer and Scanner Software" link near the top of the attached article. You'll see a list of the HP printers supported, along with which capabilities (including fax) are supported.
I am not certain what you mean by "digital fax" but if you mean the ability to fax a document right from your computer, without having to perform the ridiculous step of printing a document just so you can fax it, then you should consider Brother's line of multifunction devices.
The one I use predates AirPrint but they now have a number of printers with that feature, and also fax directly from a standard Print dialog box. Brother supports OS X very well with its native CUPS interface, they are inexpensive, their ink (in the case of inkjets) is inexpensive and lasts a long time, their photo quality is at least as good as HP's, they have lifetime free technical support with people who understand OS X, and a two year warranty.
Read the reviews (Amazon for instance, but be sure to read HP's and Brother's user reviews on their respective websites as well) and decide for yourself.
I have no affiliation with them but I would not want a Mac user to make a purchase decision they'll regret
To add to John's train of thought, I have an Epson Workforce 645 that can fax a document right from the computer without first printing. This printer is AirPrint capable.
I have no affiliation with Epson.
I'm just trying to point out that if you're considering purchasing a printer with this capability, there are plenty of choices.