Her most recent Instagram post was yesterday, with Rivera uploading a sweet selfie of herself and Josey with the caption, "just the two of us".
According to local media, Rivera's son told investigators that he and his mother were swimming, but she never got back into the boat.
Divers immediately started searching the lake, but so far there's no sign of Rivera.
Rivera shares Josey with her ex-husband Ryan Dorsey.
The pair were married in 2014 but finalised their divorce in 2018 and share joint custody of their son.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• 0800 543 354 (0800 LIFELINE) or free text 4357 (HELP) (available 24/7)
• https://www.lifeline.org.nz/services/suicide-crisis-helpline
• YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757 or TEXT 4202
• NATIONAL ANXIETY 24 HR HELPLINE: 0800 269 4389
There are lots of places to get support. For others, click here.