Chlorine has 7 outer electrons...which in turn, means it can have 7 ligands. Which in turns means make a double with carbon. Who says it has to be an alkene? Carbon has 4 electrons to share, Cl has 7 to share....it is POSSIBLE (though I have never seen it) for that molecule to exist.
But, to adress the original question, no, you are completely wrong. That is not even a possible dot structure as you aren't accounting for all the electrons. Your structure says Cl has 6 electrons while carbon has 5. In Cl, 4 unshared...2 shared in the bond. In C, one in the C-C bond, 2 not bonding, in 2 in the bond. Now, if you were to put one more dot on Cl, it would have 7 electrons: 5 unshared, 2 shared in the bond and take one dot away from C, that dot structure would work. Its not a matter of organic naming.
But, your whole idea is all wrong. The reason being is b/c they are two completely different molecules. Isomers...yes. The book says, the first Carbon has 2 H and is double bonded to a C, which has one H and a Cl bonded. You are saying the first C has 3 H, single bonded to a C, which is double bonded to a Cl. In general chem, you deal with isomers a little, but not like in organic. In organic: CH3-CHOH-CH3 is a different compound that CH2OH-CH2-CH3 even though they have the same molecular formula of C3H8O.
Also, always keep energy in mind. The reaction that will take place is the one that will take the least amount of energy. Cl only had one unpaired electron. C has four. It take far less energy to make 4 bonds in C than it does to make 2 (the double bond you drew) in Cl. There for, the more likely molecule will be the one the book drew. So, for you dot structure (not including the fact that you gave C one too many electrons), C shouldn't have any unshared electrons...and you have it is one. Now, assuming it had 3 more carbons, the molecule could have a couple of correct dot structures.