Correct/Polite way of asking "Can we speak in chinese?" I would like to preface this by saying I'm Australian and speak with an Australian accent when I'm speaking English which can be hard to digest for a lot of people new to Australia.

A lot of 1st gen Chinese-Australians struggle with my accent so I commonly find it easier to order in Chinese. This is how I would normally transition between the two languages:

我：你会说汉语吗
他：我会说
我：我要...  

I feel that this is kind of a harsh transition but haven't been corrected; yet. I've considered saying something like: 我们可以说汉语吗 but it doesn't sound overly natural or correct. 

How would I politely ask to continue the conversation in Chinese?
In eastern asian languages, hints are very important, thus, if you have already said "你会说汉语吗?", it has included an indication of "让我们说汉语吧" and the part you are asking for is actually an unnecessary part of the communication. You can just switch to your Chinese mode after that sentence as a notice.

It is the same case in English. When you say "Can we speak in Chinese?", obviously you are not inquiring if we really have the ability to say Chinese, rather, it is an indication including the sentence "Let's speak Chinese.", which you will not speak aloud.

But it is important you know the correct answer. “（咱们/我们）能用（普通话/汉语）说吗？”