WRONG
We must decide by the end of the month whether or not we’re going to do it.

This is an example of a very common mistake. In this sentence “or not” is unnecessary.

RIGHT
We must decide by the end of the month whether we’re going to do it.

Here are some other examples. In each case just “whether” is enough:

He asked me whether or not I was interested in a posting to Hong Kong.
It depends on whether or not we find a buyer in Moscow.
Whether or not my phone will work depends on me finding a charger.

Sometimes, however, “whether or not” is correct. Have a look at this sentence:

He said he can finish the project this weekend whether or not the server is down. His family is away and he can work at home.

Here “whether or not” has the same meaning as “regardless of whether”.

More examples:

The party will be outside whether or not it rains. We’ve put an awning up over the terrace.
Overall profits are up so much that apparently we’ll be getting a bonus this year whether or not we’ve met our individual targets.