Be aware, though, that there is no guarantee they will allow you to re-enter Canada after you "take a break" to go back to the UK for awhile. You are visa-exempt, but you must still demonstrate on entry that the intention of your visit is only temporary and that might be a bit difficult to do if you admit to having a Canadian born child.
My suggestion -
apply to extend your visitor status, regardless. Send it overnight by FedEx if you have to, and get delivery confirmation! As long as your application is
received by CPC-Vegreville PRIOR TO expiration of your current status, you have "implied status" to remain in Canada until a decision is made. And if you and your partner have been living together for at least one year so that you qualify as common-law partners, she should file an application to sponsor you for permanent status. If you file
outland, you're free to travel - if you file
inland you must stay in Canada for the duration of the process (which is 12-18 months). Most importantly, if you've
not yet lived together for a year, your leaving Canada now for "a break" could adversely affect your ability to qualify later as common-law partners if you don't intend to marry her.