Yes, you can use เพิ่ง for an event that happened a little while ago. You can say ฉันเพิ่งย้ายบ้านไปประเทศแคนาดา

You can use the word "เพิ่ง" for events that just happened. However, the duration should match the type of events. - "เพิ่งตื่นนอน" is O.K. if it was 10, 15 minutes ago but I will not use "เพิ่งตื่นนอน" if I already woke up for an hour. If my daughter said "เพิ่งตื่นนอน" after she woke up for an hour, it will give a feeling that she is not ready to do things such as reading, ... yet. - "เพิ่งย้ายไปแคนาดา" is good if it happen a few months ago e.g. "เพิ่งย้ายไปแคนาดาสองสามเดือนที่แล้ว". Six months may be O.K. if you fell that you are still new to the place. Moving is a major event.

เพิ่ง can be relative. You can used it with something that just happened a few seconds ago as well as something that happened a few weeks ago... or even last year! ฉันเพิ่งย้ายไปแคนาดาเมื่อปีที่แล้ว - I just moved to Canada last year (in a more casual speech you can drop the word ประเทศ)

Hi. If you want to learn Thai you can talk with me.