JWST observations have uncovered a new population of red, compact objects at high redshifts dubbed 'Little Red Dots' (LRDs), which typically show broad emission lines and are thought to be dusty Active Galactic Nuclei (AGN). Some of their other features, however, challenge the AGN explanation, such as prominent Balmer breaks and extremely faint or even missing metal high-ionization lines, X-ray, or radio emission, including in deep stacks. Broad-line AGN are known to vary in time, which is why we take advantage of two years of available JWST observations of the multiply-imaged $z=7.045$ LRD A2744-QSO1, with lensing-induced time delays between the three images spanning 22 yr (2.7 yr in the rest-frame), to investigate its photometric and spectroscopic variability. We find the equivalent widths (EWs) of the broad H$\alpha$ and H$\beta$ lines, which are independent of magnification and other systematics, to exhibit significant variations, up to $18\pm3$ % for H$\alpha$ and up to $22\pm8$ % in H$\beta$, on a timescale of 875 d (2.4 yr) in the rest-frame. This suggests that A2744-QSO1 is indeed an AGN. We find no significant photometric variability beyond the limiting systematic uncertainties, so it currently cannot be determined whether the EW variations are due to line-flux or continuum variability. These results are consistent with a typical damped random walk (DRW) variability model for an AGN like A2744-QSO1 ($M_{\mathrm{BH}}=4\times10^7 \mathrm{M}_{\odot}$) given the sparse sampling of the light-curve with the available data. Our results therefore support the AGN interpretation of this LRD, and highlight the need for further photometric and spectroscopic monitoring in order to build a detailed and reliable light-curve.