what does the carrot seed packet say re sowing? I don't tend to do mine until mid May and if frost forecast I put fleece over. Not sure about courgette as I start mine in pots in the greenhouse and put them out late May.

I would go for Eileen's suggestion of putting out your courgettes out in late May. They need to be reasonably big as the slugs will be waiting to give them a hammering. Pellets should sort them out then.