Ok, it's v good that you plan to take it really slow, but - if I'm being brutally honest - I think it may not be the best idea to do a half marathon while pregnant if you're not properly trained. And if you've only done 10 miles as your longest run before the race, then that's not ideal, pregnant or not ... Sorry if that sounds harsh.
If you're prepared to walk large sections and honestly don't care about your time then go for it, but I suspect you're going to find the long gradual climb around 8-10 miles, as you pull up to the coast at Marsden, a real struggle. And that final sprint down the coast is longer than you imagine!
In pregnancy, you're only really meant to do exercise that you've been doing already, and ease off the intensity a bit. I've done several half and full marathons but I think even I would have baulked at doing the GNR at 10 weeks - the 10k I did in the first trimester was more than enough, even though it was my slowest race in years!
If you haven't run a half marathon before, then this isn't the time to start. I mean that in the kindest and gentlest way possible.
And the GNR, as an event, is huge - so much hanging around before the start, so few opportunities to wee, huge queues for the Metro and baggage at the end - a smaller city half would be a bit more realistic, but this particular half marathon, without full training, at the end of the first trimester? Are you sure?
I deferred my GNR entry in 2012, when I was 36 weeks pg (not the plan when I entered!) and ran it the following year instead. Seeing my DS on the finish line was beautiful, and it was also a really good way to get back into running postnatally.
Have you considered deferring a year? And if not, can you honestly say you're happy to walk large sections?
Very best of luck in whatever you decide. I hope you take this post in the supportive spirit in which it's intended, and also hope your training tonight went well.