I have HP Laserjet 1020 connected to Airport Express and, after installing HP drivers, can print from MacBook Air. But there is no way to print from iOS devices because they need AirPrint compatible printer. Firstly, i installed handyPrint on mac, and everything was fine, but it works only when mac is on. So I tried and Printer Pro Lite application on iPhone. App can see printer but doesn't print anything. So I try to understand is there any possible way to tune my printer as AirPrint printer to print whenever I want? Or maybe install the right app on iPhone which can print?
Printer Pro won't solve the problem because
Printer Pro is the application that lets you wirelessly print from the iPhone. It can print directly to many Wi-Fi printers and to any printer attached to your Mac or PC via helper application installed on your computer.
If you search for "HP print" in the App Store, there are quite a lot of hits. HP All-in-One Printer Remote looks kind of helpful (but I can't test it myself).
If you don't mind jailbreaking, you can install TruPrint. This will let you AirPrint to most printers connected to a network automatically.
With TruPrint, you can print to most network printers! Simply install, and use Apple's built-in print menu. New printers will now show up thanks to TruPrint!
I've not seen any emulation software for printers that "tune" them to support the AirPrint network printing protocol on top of old HP hardware. That would be workable for a network printer, but the 1200 doesn't even have any network hardware, so you still need a device similar to AirPort to advertise the printer on the network as an AirPrint device and then subsequently translate all the print actions into legacy printing language or possibly postscript.
My guess as to your best bet is to pick a reputable AirPrint software package to run on OS X since it's cheaper than the alternatives.
There are many others besides printopia and possibly packages that run on other OS, but for my time+hassle equation it fits a sweet spot. It's easy to ask someone if $20 is worth the hassle of saving all their files to dropbox or similar and then printing them later. People also seem to get that printing won't work if the computer bridging the AirPrint request to the legacy printing format is not running.