If possible, making the acyl imidazolide would be preferable as it should give a cleaner coupling and a straightforward workup.

Your plan of using DCC/DMAP in DCM is good enough for starters. I suggest that you mix the acid and the alcohol in anhydrous DCM, add DMAP, cool the mixture in an ice bath, and add the solution of DCC in DCM. Once formed, DCU will precipitate in the course of the reaction. Given the structure of your carboxylic component, the reaction might take up to overnight. Once the reaction is complete, filter off DCU and wash it with some DCM, evaporate the solvent, and purify your product. If this does not work, a more aggressive activation method should be used. Bear in mind that activated esters such as N-hydroxysuccinimide esters work poorly with alcohols. The mixed anhydride method should be more efficient than DCC. The last resort will be converting the acid to acyl halogenide using SOCl2 or oxalyl dichloride. Whatever you do, do not use amines with strong nucleophilic properties such as N-Methylimidazole in combination with your alcohol that bears a primary alkyl bromide function. The formation of an alkylation side product seems inevitable.

Good luck

That´s okay I´d say.

If it doesn´t work, you could also use the Mitsunobu reaction. This way, you activate the alcohol for the nucleophilic attack of the acid, which in your case I think could be more appropriate.

Good luck!