Emission spectra of the carbon dot depends upon the following:

1. Size of particles.

2. Functional group attached to the carbon dot (consists of the process adopted).

3. The condition in which carbon dots are analysed. 

The theoretical aspect stands firm in almost all the time, although the further modulation with emission spectra can be possible if you can tune with the above parameter as well as pH of the measuring condition.

https://doi.org/10.1016/j.mattod.2015.11.008

To understand basic fundamental kindly go through this work:

Semiconductor Clusters, Nanocrytals and Quantum Dots (A.P.Alivisatos)

Science, Vol 271, No. 5251, 1996, 933-937

coming back to your query:

try to optimise with solvent and pH (most possible solution)

after that look for different particle size, you may obtain shift in the PL spectra (for sure).

Temperature also play significant role so keep temperature at one scale during study.

 I do not know which spectrophotometer you used.

But if we are talking about the device, then the cheapest and reliable in operation up to 800 nm device CM-2203 SOLAR, suitable for this purpose, is produced in Minsk. In my opinion, according to your order, they can make a device with sensitivity up to 1000 nm.

https://www.nature.com/articles/nnano.2009.294