No need to cut pill to half instead can take on alternative days.
Anyway if your doctor is one who prescribe levothyroxine based on TSH value alone then its of no use and need to find another.
Check your Free T4, Free T3 and TSH also Vitamin D3, B12 and Ferrotin levels. These all is connected with thyroid and simply supplying thyroid hormone alone will not bring any major differing in hypothyroid symptoms. Many of the fatigue symptoms can be linked to low blood count and that itself is related to many reasons.
I understand exactly why it's a big deal for you when you're trying to conceive, however, it's not the levothyroxine that's causing your period to be late; it's being hypothyroid.
12.5 mcg of levothyroxine is a very small dose - basically a starter dose. Did your doctor indicate whether s/he might be planning to increase your dosage, after a certain amount of time?
I don't want to scare you, but if you would happen to get pregnant and not have enough thyroid hormones, miscarriage is entirely possible. Thyroid hormones are essential for the growth and development of a fetus, so it's important that you not try to get pregnant until your hormone levels are optimal. If you're able to support a pregnancy, a fetus is dependent on the mother's thyroid hormones until about the 14th week of pregnancy, when its own thyroid kicks in, but it's still important that the mother maintain adequate levels throughout the pregnancy, because the fetus can't produce enough on its own, so the mother has to have enough for both.
Would you be able to post the results of your most current thyroid labs? Please include the reference ranges, since those vary from lab to lab and have to come from your own report, for the best comparison. Your doctor should have tested you for Free T4, Free T3 and TSH, at the very least. Hopefully, s/he would also have tested you for thyroid antibodies to determine if you have Hashimoto's.
Once we see your actual hormone levels, we'll be able to tell you if they are adequate or not. Many doctors believe that as long as results fall within the normal ranges, everything is fine, but that's not the case... We're all different and we each have our own optimal levels, but there are some guidelines.