Is that onlt 11a on your laptop? If the iPad is an iPad 3 or newer, it IS twice as fast. Apple products are 20MHz only in 2.4GHz, but can utilize 40MHz in 5GHz (except for the iPhone 4 and iPad 2, which are 65Mbps in 5GHz also, but the iPhone 5, 5s are 150Mbps as are the iPad 3 and 4. The Air maybe have moved to dual stream adapter, I don't remember and the iPhone 6/6+ and Air 2 can do 150/433Mbps depending on 11n or 11ac in 5GHz, though the Air 2 might be 300/867Mps in 5GHz, not sure).
5GHz for iOS devices:
iPad 1, 2, 3 - single stream, narrow channels, a/n
iPad 4 - single stream, narrow channels a/n # iPad4 might support wide channels, but IIRC they don't, as it was basically a rush job to get the A6X and Lightning connectors, otherwise skin job on the iPad3
iPad Air - dual stream, wide channels, a/n
iPad Air2 - dual stream, wide channels, a/n/ac
iPad Mini - single stream, wide channels, a/n
iPad Mini2 (Retina), dual stream, wide channels, a/n
ipad Mini3 - dual stream, wide channels, a/n
iPhone 5 - single stream, wide channels, a/n
iPhone 5s - single stream, wide channels, a/n
iPhone 6/6+ - single stream, wide channels, a/n/ac
iPod Touch 5th Gen - single stream, wide channels, a/n
Apple TV 2nd/3rd Gen - single stream, narrow channels, a/n
All are narrow channels in 2.4Ghz, the Air/Air2/Mini2/Mini3 are dual stream