B2 visa valid for a year, but passport got WT/WB stamp at airport?

You should do one of the following before the December date that I assume is stamped or written into your passport:

• Get your entry record corrected. You were admitted under the visa waiver program, but you should not have been because you have a B-2 visa.
• leave and re-enter the US.

When you enter the US in the future with a visa, open your passport to the page bearing your visa before handing it to the immigration officer. This will reduce the chance of an incorrect admission record.

To get your entry record corrected, you can present yourself at a deferred inspection site. These sites are for those who "believe that the documentation and corresponding endorsements issued at the port of entry require review and possible correction" (among others):

The Deferred Inspection Site staff is also available to review and issue the necessary documents to remedy errors recorded on arrival documents issued at the time of entry to the United States relating to improper non-immigrant classification, inaccurate biographical information or incorrect period of admission, if appropriate. Any designated deferred inspection location or CBP office located within an international airport should be able to assist you, regardless of where the actual document was issued.

Travelers are encouraged to contact sites not located within an international airport to establish an appointment, if necessary. In many instances, the location of your final destination where the discrepancy will be resolved may not be the port of your first arrival into the United States. Mail-in procedures are generally not available.

The Deferred Inspection Sites will only correct errors made at the time of entry. You must contact U.S. Citizenship and Immigration Services (USCIS) if you wish to: replace a lost, stolen, or mutilated Crewman's Landing Permit, CBP Form I-95; apply to extend your stay in the United States; or, change your immigration status. Specific information can be found on the USCIS website.

If instead you decide on a quick trip to Canada, Mexico, or the Caribbean, you should mention explicitly to the officer that you were admitted under the VWP even though you had a valid visa. Otherwise, the officer might readmit you for the balance of your initial admission period, since that is the usual procedure for VWP travelers who make quick trips to Canada, Mexico, or the Caribbean.

You should also be aware that a 1-year visa does not entitle you to remain in the US for a year. The duration of admission for B-2 visitors is normally six months. If you are planning to spend more than six months in the US in total, you may well have some explaining to do.

Also note that your last visit to the US need not end before the expiration date of your visa: the period of admission is independent from that. For example, if your visa were valid from 1 September 2019 until 31 August 2020, you could in theory begin a six-month stay on 31 August 2020. The likelihood of this being permitted depends in part on how much time you've spent in the US in the recent past.

As an example of someone who did understand that the visa's period of validity doesn't dictate the duration of each stay, yet who nonetheless got into fairly serious trouble, you may be interested in the story of Baxter Reid. Even the journalist reporting the linked story repeats his misunderstanding of the visa rules:

Sydney man Baxter Reid, 26, was in the US on a five-year visa and had travelled to Canada as part of a requirement for him to exit and re-enter America every six months to keep his visa valid.

A visitor visa does not authorize someone to stay in the US for the duration of the visa on the condition that they leave and return every six months; rather, it authorizes them to apply for entry during the duration of the visa. At each application for entry, the immigration officer determines whether the applicant is in fact a temporary visitor. Someone who is spending more time in the US than out of it is likely to be seen as not a temporary visitor.

If a visitor is admitted in B-1 or B-2 status, the immigration officer grants a period of admission of six months to one year (8 CFR 214.2(b)(1) and 8 CFR 214.2(b)(2)). This can be extended without leaving the country by filing an application with USCIS, but that option is not available for VWP visitors.

UPDATE. I call the LAX cup office and a very helpful man helped me understand the situation. It is basically what you guys said (thank you!!), that I can stay here for as long as my I94 allows and the stamp on my passport isn't as issue. I will bring a copy of the I94 when I leave just incase. Thank you to everyone to helped me understand this!

Hi and sorry for my absence. I called and emailed the CBP but am waiting for a response. Tomorrow I will call again to see if anything has been done. I am here for a ballet program that runs until the end of May. It does not culminate in any degree or qualification, so I cannot get a student visa, and I am also not being paid to dance here and instead have to pay fees myself. All the international dancers here are on the same visa as me. Some have had issues re entering the US as you have seen yourself how the program can be misleading and cause authorities to second guess our intentions here. However I have a confirmed flight home and proof of ties to Australia to prove I do not plan to try and fool the system! My plan is to bring all these documents with me for when I re enter after a few days in Canada in March, as well as my 1-94 form saying I was in fact admitted under my B2 visa in September. I told the people at LAX that I was coming here to dance for 9 months, and they didn't ask any more questions.