If you think that giving greater than your contractual notice period will mean that you will be on better terms, and more likely to be able to get PT and holiday work - then what's the downside?
On the other hand, you never know how an employer will react. To be brutally honest, they really may not give a toss, and could be quite surprised that you are actually giving them notice. You may be disappointed if they actually tell you that there is no need to give them extended notice.
Before I left my job to go to university, I gave my contractual 4 weeks notice. The company made no effort to do anything in the way of finding a replacement. The handover was done on my last day and I was told that I was the first person in the history of the firm to give notice. Every other employee had either resigned with immediate effect (in breach of contract - but as if they would bring a suit on that), or had just stopped turning up to work with no contact.