Yes, allergens stay in your system for a couple of weeks, and then might take a couple more weeks to clear the baby's system. I think it's a bit soon to be trying to reintroduce things.
I basically did the crazy Dr Sears elimination thing. It was v.v. hard, I lost a lot of weight, and I wouldn't recommend trying this unless you are desperate!
In my case, I was feeling quite desperate at the time. DS was about the same age as your baby, I'd eliminated dairy and eggs and seen a huge improvement, and was keeping a very detailed food diary, but there just seemed to be too many variables and I was at my wits end with worry about him. He had odd days when he seemed quite well in himself, but he still had open, weeping, infected eczema all over his body, was often very poorly and unhappy and still occasionally had some very scary breathing problems.
I don't regret doing the elimination diet, because I did eventually identify pretty much all of his allergies this way, and he became a fairly normal little baby with perfect skin - but this is certainly NOT a thing you should undertake lightly, and of course everybody will tell you are crazy if you do it.
I think in your position, as you are already suspicious of wheat, I would try excluding that for a few weeks first. Wheat is a particularly difficult one to exclude. You might see an improvement - but then if you don't see any improvement at all you might be able to conclude that wheat is not contributing to the problem, and have the bonus of keeping on eating wheat if you do decide to proceed to the more extreme elimination diet.
It's well worth keeping a careful food diary (e.g. if you put jam in your rice-milk porridge, make a note of whether it was strawberry jam or raspberry jam). Write down on each day what your baby's eczema was like, and how well she seemed generally. That way you can go through it in weeks to come and look for patterns if necessary.
I wish you much luck with all this. So sorry this is happening... but it's great that you have a doctor who is taking you seriously.