bit.ly urls

I need to create a bit.ly short URL for my photography biz.  Is there a 
safe[1] site that will search ALL domains (not just the popular ones) 
that allow anyone to register a domain (not limited to companies in that 
country only) to see if a URL is available?

jc

[1]  meaning they don't immediately register the domain you just 
searched for, hoping to con you into paying them to ransom it when you 
decide it's the one you want, only to find that it was suddenly newly 
registered.
-- 
Eat sushi frequently. - Avi
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