“Donut” doesn’t sound like “do not,” but there are puns. “I donut know what I’d do without you” is a jocular saying that has been printed on many images.
 
“I donut know what I’d do without you” was posted on Twitter by 𝔟𝔦𝔟𝔩𝔢𝔤𝔦𝔯𝔩 on September 27, 2010. “@zoecallaro I doughnut know what I’d do without you 😏🍩” was posted on Twitter by Hunter Fisher on February 4, 2013.
 
The donut saying became popular by 2013 and 2014.
   
     
Twitter 
𝔟𝔦𝔟𝔩𝔢𝔤𝔦𝔯𝔩
@BibleGirl666
I donut know what I’d do without you. <33

http://yfrog.com/j9nvmnj
1:44 PM - 27 Sep 2010
   
Twitter
Dan J Kroll
@DanJKroll
Happy 75th birthday to @KrispyKreme—I donut know what I’d do without you. 😉
12:34 PM - 13 Jul 2012
 
Twitter   
Hunter Fisher
@HunterFisher21
Replying to @zoecallaro
@zoecallaro I doughnut know what I’d do without you 😏🍩
8:17 PM - 4 Feb 2013
     
Twitter 
stevie
@stevmben
@AutumnBennett_ cause i donut know what i’d do without you
6:06 PM - 11 Feb 2013
 
Twitter
Sara Boley
@saraboley00
I “donut” know what I’d do without you! Happy Valentines Day Honey Boo!!!! 😍😘😍😻👄💏💑💘❤💌💕💖💞💓💋💗💍💝 http://instagr.am/p/VuTnP6RWbO/
2:45 PM - 14 Feb 2013
   
Twitter
Alyssa Szeto
@alyssazeet
Uhmmm best mom ever. “I donut know what I’d do without you” love ya mom. 😘💖 http://instagr.am/p/VuerGcAI1z/
4:20 PM - 14 Feb 2013
 
Twitter
Jordynne Kies
@JordynneKies
Hey Alicia I doughnut know what I’d do without you(; #StolenFromMyGirl @aliciasilberger
5:05 PM - 20 Mar 2013
 
Daily Record (Scotland, UK) 
Donut walls are the latest must-have for your wedding day
FORGET a traditional cake, get ready to go (do)nuts for a brand new wedding craze.
By Mary Palmer
13:53, 31 AUG 2016 UPDATED13:54, 31 AUG 2016
(...)
Donut walls are pretty and colourful and, in some cases, can be decorated to look very romantic. They also pave the way for an excellent pun or two ... “I donut know what I’d do without you” being one of our favourites.

Google Books
Mission Entrepreneur:
Applying Lessons from Military Life to Create Success in Business Startups
By Jen Griswold    
Coral Gables, FL: Mango Publishing Group
2017
Pg. ?:
Plus, you can see it in the cute t-shirts that customers are proudly wearing that say, “Donut know what I’d do without you.” Sugar Shack’s WHY oozes from every possible corner of their donut shop.
 
Google Books
Title I Donut Know What I’d Do Without You (6x9 Journal): Lined Writing Notebook, 120 Pages—Pink, Turquoise, Teal
Author Perky Bird Journals Staff
Publisher CreateSpace Independent Publishing Platform, 2017
ISBN 1544732791, 9781544732794
Length 120 pages
 
20 December 2017, Cincinnati (OH) Inquirer, “Madeira schools,”  Community Press/Northeast, pg. 3A, col. 3:
This year’s theme, “I Donut Know What I’d do Without You,” was carried out through a photo booth with props, table decorations, and activities.
 
Bustle
15 Punny National Sisters Day 2018 Instagram Captions That Are Just Plain Funny
By BRANDI NEAL
August 4, 2018
(...)
12. I doughnut know what I’d do without you.
 
Elite Daily
20 Witty Best Friend Quotes, Because Your ‘Gram Is Brighter With Her On It
BY JASMINE VAUGHN-HALL
August 30, 2018
(...)
20. “Donut know what I’d do without you.” — Unknown