A decent PA would do it, and give you the possibility of plugging in microphones also, or other sound sources. If you are trying to go cheap and compact, then a keyboard amp or electronic drum amp would also work, but those are normally designed for a single sound source.
You'll want a lot more watts in your PA or keyboard/drum amp than your guitar amp, because for drum sounds you need headroom and also more low frequency extension, both of which require more power. You should shoot for 200 Watts or more (total across the whole system), depending on what you can afford.
If you want to go the PA route, I'd get a 6 - 12 channel UNpowered mixer and two powered speakers. The advantage in powered speakers is you don't have to take a lot of time matching power amp to speaker cabinets. I'd look for powered speakers with at least a 12" woofer (if not 15") and 100 - 200 Watts each speaker.
For a keyboard or drum amp, I'd look at 12" designs with 200 Watts or so of total power.
Oh also, you'll need a way to get the sound from the iPad into the PA or amp. The cheapest way is find the right cable to go from the headphone jack but I can say from experience it won't sound as good as the best way. The best way is to get an iPad compatible interface (if it's "Core Audio Compliant" it will work even if it doesn't say iPad on it) and an iPad camera connection kit if it's a USB interface.