Doctor; I Have A Serious Question; I Met This Young

Doctor; I have a serious question; I met this young lady who is aged 18 years old; in early January of 2016; we had RAW SEX and it took us 4 months without meeting again; later after 4 months we met and she told me she became pregnant; by the beginning of the second week of September that same year she gave birth.

My question is;

Is it possible for a woman to get pregnant in early January of 2016 and give birth naturally without any problem to a healthy baby in early September of 2016?

I would like to find a justifiable course to file for paternity test when am 100% very sure that it is IMPOSSIBLE; otherwise if it is possible I fear to do such test which may ruin my relationship with this lady and I love her so much and I love our son so much.

Your quick response will be highly appreciated.

Regards,

Ifrah,

AFRICA/RWANDA/KIGALI