Yes, because Jump is a skill with the Movement Label (which is what matters not whether or not it's a Short Movement Skill) and nothing says you can't. Remember you'll only Jump at half your Movement value (so a 4-4 Trooper will Jump 2" while Prone).
You couldn't in N3 but the restriction in that was under effects for Prone, which appear to have been removed in N4. Looks like you can execute push up jumps in N4.
