When do you need a medical as a CFI?
14 CFR 61.23
(a) Operations requiring a medical certificate. Except as provided in paragraphs (b) and (c) of this section, a person--
(3) Must hold at least a third-class medical certificate -
(iv) When exercising the privileges of a flight instructor certificate, except for a flight instructor certificate with a glider category rating or sport pilot rating, if the person is acting as pilot in command or is serving as a required flight crewmember
(b) Operations not requiring a medical certificate. A person is not required to hold a valid medical certificate--
(5) When exercising the privileges of a flight instructor certificate if the person is not acting as pilot in command or serving as a required pilot flight crewmember
How long is it valid?
(d) Duration of a medical certificate.
(1) A first-class medical certificate expires at the end of the last day of -
(iii) The period specified in paragraph (d)(3) of this section for operations requiring a recreational pilot certificate, a private pilot certificate, a flight instructor certificate (when acting as pilot in command or a required pilot flight crewmember in operations other than glider or balloon), or a student pilot certificate.
(3) A third-class medical certificate for operations requiring a recreational pilot certificate, a private pilot certificate, a flight instructor certificate (when acting as pilot in command or a required pilot flight crewmember in operations other than glider or balloon), or a student pilot certificate issued -
(i) Before September 16, 1996, expires at the end of the 24th month after the month of the date of examination shown on the certificate; or
(ii) On or after September 16, 1996, expires at the end of:
(A) The 36th month after the month of the date of the examination shown on the certificate if the person has not reached his or her 40th birthday on or before the date of examination; or
(B) The 24th month after the month of the date of the examination shown on the certificate if the person has reached his or her 40th birthday on or before the date of the examination.
So, to summarize:
To be a CFI and act as PIC - third class medical or medical certificate that allows you to exercise third class privileges.
To be a CFI and not act as PIC (i.e. teaching a commercial student in an aircraft in which he is already rated, he is PIC) - no medical required.
First class medical is good for third class privileges for 36 calendar months.
To answer your question:
Yes, you can act as a CFI as soon as you pass your checkride. But you better know Part 61 if you want to pass the checkride.