Easy peasy...
Half distance to Pluto = 20AU= 2991960000000m
1g ~ 10m/sec^2
If we use speed/distance/acceleration formula and start with 0 speed...
...it boils down to 0.02c for 1g across 20AU. (v=27848088km/h. Speed of light is 1080000000km/h) . Not even enough to experience relativistic effects.
Can I get my friday beer now?