Do my common-law partner and I file our return at the same time even if we are both small business owners (owning separate businesses individually)?

It’s usually better to prepare your returns separately so that TurboTax can handle spousal transfers & credits for you. But if you want to prepare your returns separately, feel free to do so. Please be aware, though, that if you file at different times, the CRA will wait for the 2nd spouse’s return before looking at the 1st spouse’s return, so that may delay any refund the 1st spouse is waiting for.

So it doesn't matter at all that we are both small business owners in terms of filing together or separately?

No. That doesn't matter.