I am not licensed in MO - but a quick bit of research appears to indicate Missouri doesn't collect an estate or inheritance tax.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature.
You don't need to worry about estate taxes. The federal exemption is 5.12 MILLION. However, this is not really an estate tax question. The house passed to you pursuant to the beneficiary deed. Not a taxable event. Your interest accrued to you on the date of death with a "stepped up" basis to date of death value. An increase in value from date of death to date of sale may be a taxable event but only as to the increased value. In summary, You're fine, just let your tax guy (or gal) in on the details when you file.
INDEPENDENT LEGAL ADVISE IS RECOMMENDED. The forgoing opinion is based upon limited and hypothetical information. The answer provided is not intended as a substitute for legal representation and is not intended to create an attorney/client relationship.
Missouri's inheritance tax would only come into play if you owed federal estate taxes. It doesn't look like you are going to have tax liability. Please contact a tax expert to confirm this.
Legal disclaimer: This answer does not constitute legal advice. I am admitted to practice law in the State of Missouri only, and make no attempt to opine on matters of law that are not relevant to Missouri. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should never rely on this answer alone and nothing in these communications creates an attorney-client relationship. less