There are loads of tour operators that provide family package holidays in and around Lake Garda. Eurocamp operates Bella Italia, a campsite with loads of amenities for toddlers and younger children and with baby and toddler friendly accomodation.
You can also opt to fly to Lake Garda and book your hotel independantly. Lake Garda lies within easy reach of Verona-Villafranca airport, approximately 15 km. The shuttle from Verona airport requires a transfer in the city centre which may not be suitable with a baby and a stroller. You can also opt to take a train from Verona.
Brescia-Montichiari is approximately 30 km from Lake Garda. The airport is connected to the rail network and by an airport coach service. Some hotels offer an airport transfer service though so it may be worth checking.
Other potential airports include Milan Bergamo airport which is about 160 km from the lake and Milan Malpensa Airport which is 248 km from the lake. If you are driving, the route from Milan is straightforward; you just take the autostrada all the way.
Flight time from the UK and Ireland ranges from between 2 and 2.5 hours. This is an ideal time for travel with toddlers.