Okay to get a tattoo while breastfeeding and weeks after c-section?

I'll be having a c-section around May 8th and my birthday is May 21st.. I am really wanting to get a tattoo with my girls names on it for my birthday but I think that will be to soon? I'll be breastfeeding also. 
Here is what I'm wanting to get. I would be getting it at a shop that I research to make sure they follow the rules and are clean.. 
I'll ask my doctor next week about it.. 
It's not a big deal if I have to wait just wasn't sure on the wait times after and if it was even okay to get one while breastfeeding which I'll be doing for at least a year. 

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