I would think Glóin and Gimli made their way from Erebor through Mirkwood, then to the Carrock and the Pass of Imladris. That was the "High Pass" referred to by Glóin in his conversation to Frodo in Rivendell.
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'Indeed,' said Glóin. 'if not for the Beornings, the passage from Dale to Rivendell would long ago have become impossable. They are valiant men, and keep open the High Pass and the Ford of Carrock.'
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Many Meetings
Since that route was known to be safe, it seems logical that's the way the Dwarves would have taken.