Should I file for child support?

Hi guys. When I was pregnant, I read an article where the author said that child support can be a reminder to the deadbeat parent that he/she has a kid and eventually “grow up” and want to be responsible. So I thought, Imma file for child support. I wont need his money but this way, there wont be any blame on my part. My ex actually has been texting me at least once a week and talks about himself (rarely asks about my daughter) and plays victim when I cant pick up his call so he can talk about his self again (coz boy its hard to be a single mom with 0 help). Maybe that counts as “responsible”. But reality kicked me. My baby is breastfed and 2mos old so she doesn’t have a lot of expenses YET. Right now, I have a few $$ left with my salary after expenses. But with all my plans for this year plus her future needs, my salary wont be enough. I really don’t want to even get any support from him. I want to be able to say that I raised my daughter by myself (kinda prideful). I know I wont get a lot but the tad bit is helpful. I cant have double jobs coz im in the military. Getting out isnt an option either. My pro is $. My cons are pride and I was told that I have to ask my ex permission if I want to take her outof the country which will be hard coz of my line of work plus the career I want (foreign diplomat). Does anyone know if this is true? And should I file for child support and custody? Or dyou think I can do it all alone?

To all single mamas out there, other than a double job, what else did you do to make it out there?