Disclaimer: I am not a healthcare professional nor have I undertaken any medical training whatsoever. If in doubt, consult your doctor or a nutrition specialist.
Firstly, I think you can find interesting answers to your question in another question on this site which is, however, concerned with vegan pregnancy. What this basically means is that you can subtract vegan related problems from the answers and be left with the vegetarian related ones.
I will try to address your question in my own answer as well:
The reason that you have included as the one because of which your baby would suffer from defects in its nervous system and brain - the difference of protein found in meat/fish as compared to vegetarian sources - is, as far as I know, unfounded. It is true that the overall amino-acid composition differs among these groups, but with balanced vegetarian diet you can meet the target for each of the essential amino-acids - the stuff from which protein is synthesized.
In fact, in a correspondence from Dr McDougall to AHA (The American Heart Association) it is argued that (emphasis mine)
..By calculating the amount of each essential amino acid provided by
unprocessed complex carbohydrates (starches and vegetables) and
comparing these values with those determined by Rose, the results
show that any single one or combination of these plant foods provides
amino acid intakes in excess of the recommended requirements.
Therefore, a careful look at the founding scientific research and some
simple math prove it is impossible to design an amino acid–deficient
diet based on the amounts of unprocessed starches and vegetables
sufficient to meet the calorie needs of humans. Furthermore, mixing
foods to make a complementary amino acid composition is unnecessary..
To which AHA itself responds (emphasis mine):
..We certainly agree with Dr McDougall that a vegetarian diet based on
the AHA guidelines of 5 to 6 servings of whole grains and 5 or more
servings of vegetables and fruit would, in fact, supply all of the
amino acids necessary for health...
Now as to pregnancy and vegetarianism in general, there is little else to consider, since vegetarian diet does not lack in any specific nutrient as the vegan does (eg. vitamins B12 and D). Normal recommendations, valid for non-vegetarians, apply. A list of these can be easily found in abundance of pregnancy literature and articles, such as this one from NHS. It recommends the folic acid (B9) supplements of 400mcg per day before pregnancy and for the first 12 weeks of it. Folic acid is abundant in vegetarian diet so no higher doses for vegetarians should be needed. It also suggests other possible nutrients to supplement so definitely have a look.
To reiterate, I am not a professional trained in giving medical advice and your best bet would be to contact someone who is. On the other hand, I believe that vegetarianism in pregnancy is not a risk factor, if done sensibly, and you certainly would not be the first parent(s) to go down this road. Good luck :)