"should get around" is a correct and usable phrase in written English.
It is commonly used to express the idea of reaching or accomplishing something, often with effort or difficulty. Example: "I should get around to organizing my closet this weekend." This means that the speaker plans to or intends to finally organize their closet, which they may have been putting off for some time. Another example: "I should get around to booking my flight for the conference." This means that the speaker needs to make the effort to book their flight in order to attend the conference.
"I guess I should get around to bringing in some of my stuff".
Perhaps, while you're stuck in here anyway, you should get around to sending out that stack of résumés.
"They were scandalous and outrageous, treated their fans like they were in the band, and wrote two albums that more people really should get around to listening to".
(Everyone's needs are different, but health professionals recommend that five-year-olds should get around 11 hours a night, 10-year-olds around 10 hours, and 15-year-olds nine hours).
He says his company concentrates on re-creating the bones, skeletons, and underlying structures of things that can walk or otherwise move, whether they're virtual humans, dogs, robots, or cars, and simulating how they should get around and what should happen when a user pokes or prods them.
The other 35 participants expressed thoughts that were not specifically related to body shape e.g., 'I wonder what the experimenter is thinking', 'I should get around to waxing my thighs'.
To those of us unschooled in its ancient lineage and myriad applications, yoga has always seemed like something we should really get around to doing.
I should really get around to reading Middlemarch, The Red and the Black (available in Penguin Classics, £9.99) and To the Lighthouse (available in Vintage, £6.99), which have been on my to-do pile for years now.
Also, I should really get around to figuring out his or her gender so that I can use more specific pronouns".
Only last year, 25 years since the original idea, I thought, "Well, I should actually get around to doing that thing".
It is concerned that, should it ever get around to building its space plane, the definitions in the bill may, or may not, cover its vehicle.
