Yes, you can absolutely Dash while prone. If you don't want to spend half your speed to stand up, you can still crawl (from PHB, 191)
To move while prone, you must crawl or use magic such as teleportation. Every foot of movement while crawling costs 1 extra foot.
To stand up, you use half your speed (PHB, 190)
Standing up takes more effort; doing so costs an amount of movement equal to half your speed.
What this means, and why standing up is probably better.
That is basically turning your movement into difficult terrain, which will effectively negate the dash. If you have a Speed of 30 and take the Dash action, you would now can move a total 60(30 regular move, 30 Dash), but could only move 30'. Alternatively, you could stand up for 15' of movement (half your speed), and then complete your movement (15) and take the dash action(30) for a total of 45.
A related question on the cost of standing up helps to understand this.