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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