The noun is from dog + -o (colloquializing suffix), perhaps after the adverb. The adverb is probably of the same origin.
Meanings
(Internet, childish, informal) A dog.
‘It’s OK, you’re allowed out here. There haven’t been any other doggos in this garden since …’ He shrugged. ‘I dunno, forever.’ His grandmother hadn’t had a dog, and she’d lived in the cottage for decades. ‘Doggos?’ he said out loud. ‘Did I just say “doggos”?’ 2020, Liz Davies, The Summer of Falling in Love, Lilac Tree Books:
A note of caution to readers with pets: Xylitol is toxic to dogs and can have potentially life-threatening effects. As owners of two doggos ourselves, we encourage anyone with a dog to use extreme caution when bringing xylitol into your home. 2019, Matt Dorsey, Jenny Dorsey, Healthy Cocktails, Simon and Schuster, →ISBN:
Around the same time, "wholesome" memes of cute doggos and puppers rejuvenated social media feeds that seemed daily filled with fresh horrors. 2019, Gretchen McCulloch, Because Internet: Understanding the New Rules of Language, Riverhead Books, →ISBN:
The quick, cuddly truth is there are several benefits to sleeping with your doggo or pussycat — but depending on the circumstances, there are risks you might like to consider and mitigate. 2019 January 14, Kellie Scott, “Should you let your pets sleep in bed with you?”, in ABC, archived from the original on 05 Mar 2021:
They might look pretty, but many houseplants are poisonous to your doggos and cattos. 2018 September 13, Juliette Steen, “10 common plants that are poisonous to dogs and cats”, in ABC, archived from the original on 03 Jan 2021: