Hemoglobin levels in pregnancy are the same as in any other time (above 12 if we're talking about the same units), it's just that most pregnant women become a little anemic in pregnancy anyways. It's common practice where I live to do monthly FBC (full blood check) in pregnancy for that reason and my last check was also 11.9 or something.
In general, 11.3 sounds a bit low but not usually enough to explain extreme exhaustion. At worst, it might make a regular person lose their breath a little faster when exercising. Many people have it constantly and don't even realize it unless they do a blood test. It's not a bad idea to take iron supplements as chances are that it's due to iron deficiency, a very common occurrence in pregnancy. Iron pills are also mandatory for pregnant women here, so I thought all pregnant women were on them, but I guess things are different from country to country. Anyway, iron supplements take months to work (iron builds reallllllllly slowly in our bodies), so it's not urgent either if you wish to wait a couple of days and double-check with your doctor. They might want to check your ferritin levels (iron stocks in your body) or they might have specific protocols in place? Folate supplements are also a good idea if they are not administered already as a standard of care. Folate and iron-deficiency anemias usually lead to different red cell markers (iron-deficiency anemia lowers MCV and MCH, whereas folate and B12 deficiency tend to increase MCV and MCH, as a
very general rule of thumb). Where I live they also check for other stuff, such as being a thalassaemia carrier (which leads to low hemoglobin with high RBC count), but it's more common in Mediterranean people, so it's probably redundant in your case.
Ehm, just saying though, this is just how things are done where I live. I love giving out information, but I'm always worried of getting too carried away and leading people astray. Personally, I'd wait and talk to my OB and daze them with a million questions, lol. She will probably have more specific information for you based on the specifics of your results and the treatment guidelines where you live. It's just that there's nothing wrong with some independent research beforehand either.