Yes, you can! When travelling with toddlers and young children, though, try staying in calmer and more personable Algarve resort towns of; Alvor, Tavira, Praia da Luz and Carvoeiro. If you plan on visiting Cascais on the Lisbon coastline, just visit it outside of the busy summer season.
Portugal is very friendly toddlers and their parents. Don't be surprised if someone smiles at your toddler and says hello to them - mainly old ladies have a tendency to do that!
Keep in mind that Portugal is a very hilly country (Lisbon, Porto, Albufeira) and the decorative calçada cobbled streets are a nightmare for small wheeled buggies.
All cafes will provide free tap water but baby changing facilities may be very limited (you will find them in larger shopping centres, but in women’s toilets only). Some public places also have microwaves if you need to heat your baby's food, and most restaurants have little chairs for their little clients!
Child car seats are not mandatory in Portugal and if you don’t want to bring your own, you will have to travel with your baby on your lap in taxis. You could also opt to rent a car seat. Some companies in Lisbon also offer taxis with a car seat free of charge, but you will need to pre-book this service.
Fresh milk (leite pasteurizado) for babies is sold in larger supermarkets. Gordo is full-fat, meio-gordo is half-fat and magro is skimmed milk. Mini-markets, smaller shops and cafés generally only stock UHT milk. Formula is widely available in supermarkets also, however some brands you might be used to can be difficult to find.
Nappies/diapers (fraldas) are widely available in supermarkets and pharmacies. Pampers are sold as ‘Dadots’ and Huggies are also widely available. Local brands will also be available in small and large supermarkets.