I took a look at Carter's 1919 app for an AL pension.
He states very clearly that he enlisted in the Indian Territory in 1861 in the 3rd AR Cav., "Stand Watie, col." (!).
He then drifted into Baxter Smith's 2nd TN Cav and then to scouting with Forrest.
It contains affidavits confirming that he scouted for Forrest in 1864, and was present at the battle of Okolona where Jeff Forrest was killed.
No confirmation of any earlier service, other than his word.