Dizziness in pregnancy is pretty common, especially if you're petite like you, but since you're already feeling faint after just a walk it's worth bringing up with your PD or OB to rule out anything else like low blood pressure or iron levels that might not have shown up in routine blood tests. In the meantime, make sure you're drinking enough water, eating regularly, and not pushing yourself too hard on walks, getting up slowly from sitting or lying down helps too. Your doctor might want to do a more specific check on your blood pressure readings or recheck your iron since dizziness after light activity isn't something to brush off.
Yes this is normal for pregnant women. I experienced the same and was low in red blood count during pregnancy. My gynae asked me to take iron supplements (can buy from any pharmacy). Just take a rest in between walk if needed. Listen to your body.