I like it, it solves a common problem. It would help if you can check the availability of other domain extensions, ".me .io .co ...etc".
Also a small idea: I think hitting enter while the focus is inside the input should trigger the search action.
It would be great if the result would load faster and would contain a wider search. Good alternatives are Namecheckr (https://www.namecheckr.com) and Namecheck (https://namechk.com). I used both in the recent past a lot and they are very helpful.
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Simple but there are plenty of other services already that have a lot more checking going on... domainr.com, knowem as @Barry mentioned, Namechk.com, namevine that @nikesh mentioned... and more. What are you going to do to make yourself unique and differentiate yourself?
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I like http://namevine.com for these purposes, they include Instagram and Pintrest too , May be that would be your next integration, All the Best :)
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Useful, be handy if it shows the owner of the domain/twitter/fb accounts too (To see if they are competitors!)
Laravel Queues in Action
SuperWidget - Shortcuts & APIs
SwiftyBeaver Logging Platform
KnowEm
Valentina Studio