is there a way to search for a specific app quickly in your purchase history?

If you mean in iTunes then go to Applications and that search bar in the top right corner will do the trick

 

The thread title kinda says "purchase history"

and I don't think so, unless you check your email inbox for the receipts

 

If you right-click on the app in your library and choose Get Info, you can see the purchase date - from there you can a bit more quickly find the invoice...

 

hmm well that's true, but the purchase date shown can be the date you downloaded an update for the app, which would be way after the date you actually bought it

 

Easiest way will be search your iTunes receipts. I have set up gmail to label and group all my iTunes receipts. All I need to do is search that label for any app to see if I have it or when I bought it.

 

Nope - it shows both your purchase date and the last time it was updated.