Yes, you can play on both devices. The game automatically syncs to the cloud, so you don't need to do anything special. Just log in on both devices and it will work.
It seems to be a glitch with the game. The developers are aware of it and working on it. It would seem you can't really get them back for now, but the colours you bought are safe. I suppose you will get them back in an upcoming bugfix.
Veronica Belmont asked just about the same question to Joseph Alminawi and Garrett Peek, creators of Draw Something, on Twit.tv's Game On! aired on March 19.
Video: http://twit.tv/show/game-on/10 (approximately at 47:25)
Transcript
Veronica Belmont: I've been playing for a really long time, and I bought a lot of colour packs with the coins I've been winning, and they go away. I don't have any of my colours. I keep logging in and out, trying to get them back, and now they just won't come back at all and I'm very sad.
Joseph Alminawi: Your colours, your coins, your bombs, they're all safe. What's going on is that the game is just having a little difficulty grabbing and looking at your inventory, but we're on that right now and we should have this solved really soon.
Garrett Peek: All your coins and colours are safe; we have that all saved. It's just making the calls, since we're getting millions and millions of calls per second [it's causing trouble].
Best Answer
This question deals with recovering a lost username and/or password. So you could delete Draw Something from the iPad and re-download it, and then enter in her existing account details.
Another option might be to link the Android Draw Something to a Facebook account, and then link the iPad Draw Something to the Facebook account as well. I've done this for my iPhone and iPad and it does a good job of keeping them in sync.