Most likely "a letter from the doctor" may be requested if this is the first time
you are filing. You may also need paperwork related to the adoption itself, so that the IRS can verify the child is your legal dependent. Generally you should expect a delay in receiving any refund you are due, as the IRS will generally request information from you before finishing your return. This is not an audit - but they will still need certain requested paperwork and some additional time to process your return before issuing any money.
Generally the IRS will not want any documents sent in advance (with your return), but your case is somewhat complex because of the amount of different issues involved - adoption, disability, etc. You may qualify for a range of different credits and special tax situations, such as the Disability and Earned Income Child Tax Credit and the Adoption Credit and Adoption Assistance Programs.
I would strongly encourage you to have a planning session with a tax professional - not just a regular tax preparer, preferably one with experience with complex situations like this - as there are many thousands of dollars of tax credits, incentives, and potential penalties involved. This doesn't need to be a high-stress situation and you might have a few very nice tax years, but it's always better to get the filings right the first time and have paperwork ready in advance - as you are obviously already trying to do!
One final word of warning: be careful about issues related to the year of filing and claiming of credits/expenses. As noted in topic 607 (linked above regarding adoption), what year you can claim things varies on multiple factors (foreign vs domestic adoption, when expenses were paid, when the adoption was completed, etc.). There may be some things you can claim on this years return (taxes related to last year), and there is some you might not be able to claim until next year (taxes related to this current year). You'll need to read all the fine print closely to make sure you claim things appropriately, and again a qualified professional may be warranted if available to you. I tend to prefer to file my own taxes with tax software to assist, but be prepared for a lot of IRS publication reading if you want to make sure you handle everything appropriately!
Most importantly: congratulations on a successful adoption, and good luck! You're already doing a great job by trying to get all your ducks in a row in advance of when you really need to, which is a very wise choice.