We describe a two-laser experiment using optical-optical double resonance fluorescence and Autler-Townes (AT) splittings to determine the NaK 3 (1)Pi-->1(X)(1)Sigma(+), 2(A)(1)Sigma(+) absolute transition dipole moment functions. Resolved 3 (1)Pi-->A (1)Sigma(+) and 3 (1)Pi-->X (1)Sigma(+) fluorescence was recorded with the frequencies of a titanium-sapphire laser (L1) and a ring dye laser (L2) fixed to excite particular 3 (1)Pi(upsilon = 19,J = 11,f)<--A (1)Sigma(+)(upsilon('),J(') = J = 11,e)<--X (1)Sigma(+)(upsilon("),J(") = J(')+/-1,e) double resonance transitions. The coefficients of a trial transition dipole moment function mu(e)(R) = a(0)+a(1)(R(eq)/R)(2)+a(2)(R(eq)/R)(4)+... were adjusted to match the relative intensities of resolved spectral lines terminating on the lower A (1)Sigma(+)(upsilon('),11,e) and X (1)Sigma(+)(upsilon("),11,e) levels. These data provide a relative measure of the functions mu(e)(R) over a broad range of R. Next, L2 was tuned to either the 3 (1)Pi(19,11,f)<--A (1)Sigma(+)(10,11,e) or 3 (1)Pi(19,11,f)<--A (1)Sigma(+)(9,11,e) transition and focused to an intensity large enough to split the levels via the AT effect. L1 was scanned over the A (1)Sigma(+)(10,11,e)<--X (1)Sigma(+)(1,10,e) or A (1)Sigma(+)(9,11,e)<--X (1)Sigma(+)(0,12,e) transition to probe the AT line shape, which was fit using density matrix equations to yield an absolute value for mu(ik) = integral psi(vib) (i)(R)mu(e)(R)psi(vib)(k)(R)dR, where i and k represent the upper and lower levels, respectively, of the coupling laser (L2) transition. Finally, the values of mu(ik) were used to place the relative mu(e)(R) functions obtained with resolved fluorescence onto an absolute scale. We compare our experimental transition dipole moment functions to the theoretical work of Magnier et al. [J. Mol. Spectrosc. 200, 96 (2000)].