with the little one and on a budget

Me and my hubby are planning to escape with our one year old to a place which is breathtaking, safe and not too expensive. We would like to go in winter months for about 5-7 days. Stunning, sandy beach would be our preference. Budget isn't too high, it's around £1200 but we're not looking for expensive hotels or fancy food. Rather peace and surrounding beauty with a piece of lovely land to explore by foot.
Please recommend us something special. Thanks in advance. <3

Did I say winter months? Pardon. I meant autumn - September-October. <3