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The thermocouple should detect the heat from the flame and keep the gas valve open.
From the description this is not happening.
Before changing the valve, does the flame look fairly strong? Its possible the jet is blocked, not allowing enough gas to flow which will produce a weak flame thats not hot enough for the thermocouple to detect.
If all looks well, then, yes, you are correct, its a faulty thermocouple.
For the replacement, please see here
(Just click on the word in blue)
You should also be able to order this from a local supplier
If you need more help, please just ask.
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