Employers do have to give you a minimum period of notice under the Fair Work Act. If you are a full time employee and have been at work for less than a year, 1 week notice is necessary. If you have been at work there for more than 5 years, four weeks notice is required. That notice may be increased by one week if you are over 45 years of age.
Of course, if you are employed under an enterprise agreement or contract, that notice may be more. Your employer can make a payment in lieu of notice so long as it is at least equal to the full rate of pay you would have received if you worked out the whole notice period.
The only situation where notice is not required is where you may be accused of serious misconduct. This is called summary dismissal. The employer must be able to prove that any allegation of serious misconduct is justifiable under the Fair Work Act. If you do not believe you have been fairly treated, you may have unfair dismissal rights.
If your employer does not give you proper notice when dismissing you, you may take legal action in the Federal Circuit Court of the Federal Court to recover money owed by the employer. This usually amounts to the wages that would otherwise have been earned during the notice period.