Give Printer Pro a try. You can use the Lite version to test if you can print with the app from your iPad to your printer. It prints to many wi-fi printers as well as printers attached to your computer. If you can print the sample documents with the Lite version, then you will need to buy the pro version to print your own documents. The app is US$7 in the iTunes App Store.
I use 'Print n Share' to print to my wireless hp printer. Check out the devlopers website to check for compatibility. Mine works brilliantly. So glad I didn't have to purchase a new printer.
Printopia requires your Mac to be switched on to work. As someone else suggested look at Print n Share if you have a HP wireless printer. It will print directly to all HP wi-fi printers, and some others too.
Buy hp d110 I bought mine back in November paid 99 dollars just seen it last week at best buy for 59 dollars best printer I ever had I don't even think you need a computer to hook it up found my iPad in a second